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Online ISSN 1751-8652 Print ISSN 1751-8644

IET Control Theory & Applications

Volume 4, Issue 9, September 2010

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Volume 4, Issue 9

September 2010

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  • Regular Papers

    • Comparative analysis of two non-linear observers for estimation of tyre/road contact in the presence of imperfect measurements
      • Author(s): N. Patel ; C. Edwards ; S.K. Spurgeon
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1501 –1510
      • DOI:  10.1049/iet-cta.2009.0087
      • Type: Article
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      • p. 1501 –1510 (10)
        This study presents a comparative study of a sliding-mode observer-based scheme and an adaptive observer-based scheme designed to estimate a road surface condition parameter. The effect of imperfect measurements associated with the wheel angular velocity is explored. A detailed analytical analysis is presented and results are shown from a variety of simulations. Both schemes assume only wheel angular velocity is measured and use an observer to reconstruct the states and the road condition parameter.
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      Field-programmable gate array-based intelligent dynamic sliding-mode control using recurrent wavelet neural network for linear ultrasonic motor
      • Author(s): F.-J. Lin ; Y.-C. Hung ; S.-Y. Chen
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1511 –1532
      • DOI:  10.1049/iet-cta.2009.0066
      • Type: Article
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      • p. 1511 –1532 (22)
        A field-programmable gate array (FPGA)-based intelligent dynamic sliding-mode control (IDSMC) using recurrent wavelet neural network (RWNN) estimator is proposed to control the mover position of a linear ultrasonic motor (LUSM) in this study. First, the structure and operating principles of the LUSM are introduced briefly. Then, the dynamics of LUSM mechanism with the introduction of a lumped uncertainty, which include the friction force, is derived. Since the dynamic characteristics and motor parameters of the LUSM are non-linear and time-varying, an IDSMC using RWNN estimator is designed to achieve robust control performance of the LUSM drive system. The RWNN estimator is employed to estimate the non-linear functions including the system parameters and external disturbance. Moreover, the adaptive learning algorithm trained the parameters of the RWNN online is derived using the Lyapunov stability theorem. Furthermore, an FPGA chip is adopted to implement the developed control and on-line learning algorithms for possible low-cost and high-performance industrial applications. The experimental results show that excellent positioning and tracking performance are achieved. In addition, the robustness to parameter variations and friction force can be obtained as well using the proposed control system.
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      Adaptive law with a new leakage term
      • Author(s): S. Blažič ; D. Matko ; I. Škrjanc
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1533 –1542
      • DOI:  10.1049/iet-cta.2009.0349
      • Type: Article
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      • p. 1533 –1542 (10)
        The hyperstability theory of adaptive control systems is extended to encompass plants with unmodelled dynamics and disturbances. The analysis not only shows that leakage in the adaptive law is a natural way to avoid robustness problems (which is a known result in adaptive control theory), but also provides a new adaptive law that is a sort of signal-dependent σ-modification. The proposed adaptive law is less conservative than the σ-modification, but still ensures the global stability of the system, which is formally proven in the paper. Since it is shown that the design parameter σ′ of the proposed adaptive law is directly related to the H∞ norm of the parasitic dynamics, the criteria for system stability are derived. Based on these, some guidelines for choosing the leakage parameter σ′ and the bandwidth of the reference model are presented.
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      Neural-network-based simple adaptive control of uncertain multi-input multi-output non-linear systems
      • Author(s): T. Li ; G. Feng ; D. Wang ; S. Tong
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1543 –1557
      • DOI:  10.1049/iet-cta.2009.0214
      • Type: Article
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      • p. 1543 –1557 (15)
        An adaptive control scheme based on radial basis function (RBF) neural networks (NNs) has been developed in this study for a class of uncertain multi-input multi-output (MIMO) non-linear systems in block-triangular forms via dynamic surface approach and ‘minimal learning parameters (MLP)’ algorithm. In the algorithm, the RBF NNs are only used to deal with those unstructured system functions, whereas the unknown virtual control gain functions do not need to be estimated. Consequently, the potential controller singularity problem can be overcome. Two key advantages of our scheme are that (i) only one parameter needs to be updated online for each subsystem, and (ii) both problems of ‘dimension curse’ and ‘explosion of complexity’ are avoided. The computational burden has thus been greatly reduced. It is proved via Lyapunov stability theory that all signals in the interconnected closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking errors converge to a small neighbourhood around zero. Finally, the simulation results are presented to demonstrate the effectiveness of the proposed scheme.
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      Stabilisation for a class of non-linear systems with uncertain parameter based on centre manifold
      • Author(s): X. Cai ; Z. Han ; J. Huang
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1558 –1568
      • DOI:  10.1049/iet-cta.2008.0355
      • Type: Article
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      • p. 1558 –1568 (11)
        The stabilisation problem of non-linear systems with multi-uncontrollable modes on the imaginary axes is studied. The relation between the centre manifold and the feedback law is given. By choosing the first coordinate function of the centre manifold, a state feedback law to stabilise the dynamics of the centre manifold is acquired. It can stabilise the full order system. This method is applied to stabilise non-linear systems with double Hopf bifurcation. The simulation shows the effectiveness of the method.
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      Cooperative control of underactuated surface vessels
      • Author(s): W. Dong
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1569 –1580
      • DOI:  10.1049/iet-cta.2009.0362
      • Type: Article
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      • p. 1569 –1580 (12)
        This study considers the cooperative control of a group of underactuated surface vessels using the relative information between neighbour's information such that the group of surface vessels come into a desired geometric pattern whose centroid moves along a desired tajectory. With the aid of results from graph theory and Lyapunov techniques, decentralised cooperative control laws are proposed for different communication scenarios. The effect of communication delays on the proposed controllers is analysed. Simulation results show the effectiveness of the proposed control laws.
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      Piece-wise linear functions-based model predictive control of large-scale sewage systems
      • Author(s): C. Ocampo-Martinez  and  V. Puig
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1581 –1593
      • DOI:  10.1049/iet-cta.2009.0206
      • Type: Article
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      • p. 1581 –1593 (13)
        In this study, model predictive control (MPC) of large-scale sewage systems is addressed, considering several inherent continuous/discrete phenomena (overflows in sewers and tanks) and elements (weirs) in the system. This fact results in distinct behaviour depending on the dynamic state (flow/volume) of the network. These behaviours cannot be neglected nor can be modelled by a pure linear representation. In order to take into account these phenomena and elements in the design of the control strategy, a modelling approach based on piece-wise linear functions (PWLF) is proposed and compared against a hybrid modelling approach previously suggested by the authors. Control performance results and associated computation times of the closed-loop scheme considering both modelling approaches are compared by using a real case study based on the Barcelona sewer network. Results have shown an important reduction in the computation time when the PWLF-based model is used, with an acceptable suboptimality level in the closed-loop system performance.
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      Guaranteed cost decoupling control of bank-to-turn vehicle
      • Author(s): Z. Deng ; Y. Wang ; L. Liu ; Q. Zhu
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1594 –1604
      • DOI:  10.1049/iet-cta.2009.0114
      • Type: Article
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      • p. 1594 –1604 (11)
        This study presents a novel solution to the multi-variable coupling attitude control of a bank-to-turn vehicle. This highly widely demanded control task becomes very challenging on the vehicle's rolling capabilities while the vehicle tracks a moving target. To effectively deal with the relevant issues, this study proposes an integrated procedure to design the state-feedback decoupling controller to dynamically reduce the coupling effect. In a methodology based on linear matrix inequality, the tracking guaranteed cost control law combined with the decoupling control is proposed to accommodate the parameter uncertainties without coupling. Finally, a new strategy called augmented tracking guaranteed cost decoupling control scheme is developed to eliminate the static errors. Large cohort of simulated bench tests is provided to validate the feasibility and effectiveness of the proposed approaches. Hopefully these examples will also provide potential users guidelines for their applications.
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      Global asymptotic tracking of robot manipulators with a simple decentralised non-linear PD-like controller
      • Author(s): Y.X. Su  and  C.H. Zheng
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1605 –1611
      • DOI:  10.1049/iet-cta.2008.0423
      • Type: Article
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      • p. 1605 –1611 (7)
        In this study, the authors address the problem of global asymptotically tracking control of uncertain robot manipulators with a simple decentralised non-linear proportional plus derivative like controller. The proposed controller is formulated with a decentralised structure without reference to modelling information and the control gains are easily determined based on some well-known bounds extracted from the robot dynamics, and thus it is easy to implement. The global asymptotic stability of the closed-loop system is shown with Lyapunov's direct method. Even when the proposed scheme is modified to avoid the possible chattering in practical implementation, the overall performance remains appealing. Simulations performed on a two degree-of-freedom robot manipulator demonstrate the effectiveness of the proposed approach.
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      Stabilisability and detectability in networked control
      • Author(s): S. Longo ; G. Herrmann ; P. Barber
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1612 –1626
      • DOI:  10.1049/iet-cta.2009.0234
      • Type: Article
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      • p. 1612 –1626 (15)
        The authors reconsider and advance the analysis of controllability and observability (and the weaker stabilisability and detectability properties) of a class of linear networked control systems (NCSs). The authors model the NCS as a periodic system with limited communication where the non-updated signals can either be held constant (the zero-order-hold case) or reset to zero. Periodicity is dealt with the lifting technique. The authors provide conditions for controllability (stabilisability) and observability (detectability) of the NCS, given a communication sequence and the controlled plant model. These conditions allow to find communication sequences which are shorter than previously established. A strict lower bound for the sequence length is given. In the sampled-data case, the authors prove that a communication sequence that avoids particularly defined pathological sampling rates and particular eigenvalues can preserve stabilisability (and detectability for the dual problem) with a ‘minimum’ sequence length.
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      Sensors-less neural maximum power point tracking control of induction machines wind generators by growing neural gas and minor component analysis EXIN + reduced order observer
      • Author(s): M. Pucci
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1627 –1638
      • DOI:  10.1049/iet-cta.2009.0510
      • Type: Article
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      • p. 1627 –1638 (12)
        Subject of this work is a maximum power point tracking technique for high-performance wind generator with induction machine based on the growing neural gas (GNG) network and the minor component analysis (MCA) EXIN+neuron. The main idea is to create a fully sensors-less system, meaning a system neither with the wind speed sensors nor the machine speed sensor. The GNG network has been used, trained off-line, to learn the turbine direct characteristic surface torque against wind speed and machine speed and implemented on-line, exploiting the function inversion capability of the GNG, to obtain the wind tangential speed on the basis of the estimated torque and measured machine speed. The machine reference speed is then computed on the basis of the optimal tip speed ratio. With regard to the power conversion stage, a back-to-back configuration with two insulated gate bipolar transistor (IGBT) voltage source inverters has been chosen, one on the machine side and the other on the grid side. The field-oriented control of the machine has been integrated with an intelligent sensorless technique, the so-called MCA EXIN+reduced order observer. The performance of the adopted technique has been verified experimentally on a suitably devised test setup.
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      Theory and experiments of global adaptive output feedback tracking control of manipulators
      • Author(s): J. Moreno-Valenzuela ; V. Santibáñez ; E. Orozco-Manrı́quez ; L. González-Hernández
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1639 –1654
      • DOI:  10.1049/iet-cta.2009.0249
      • Type: Article
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      • p. 1639 –1654 (16)
        A new adaptive controller for robot manipulators is proposed. The new approach uses only position measurements. The main conclusions derived from the closed-loop system analysis are in two main results. In the first one, the global convergence of the position and velocity tracking errors is stated by using a condition that relates the viscous friction damping and the desired joint speed. In the second one, such a condition is dropped out but the local exponential stability of the closed-loop system is shown. To confirm the theoretical conclusions, a detailed experimental study in a two degrees-of-freedom direct-drive manipulator is provided, where the performance of the new controller is compared with respect to a known output feedback adaptive controller.
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      Design of robust adaptive variable structure tracking controllers with application to rigid robot manipulators
      • Author(s): C.-C. Cheng ; S.-H. Chien ; F.-C. Shih
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1655 –1664
      • DOI:  10.1049/iet-cta.2009.0194
      • Type: Article
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      • p. 1655 –1664 (10)
        Based on the Lyapunov stability theorem, a variable structure control (VSC) scheme with adaptive mechanisms embedded is proposed in this study for a class of perturbed multi-input multi-output (MIMO) non-linear systems to solve robust tracking problems. The dynamic equation of the control system contains a perturbed leading coefficient matrix, which can be either positive definite or negative definite, and the perturbation is composed of parameter variations, input gain uncertainties, external disturbances etc. By introducing some adaptive mechanisms embedded in the variable structure controller, the proposed control scheme is capable of suppressing the perturbations to achieve asymptotic stability without knowing their upper bounds except for those of the uncertainties of the input gains. An example of its application to a rigid robot manipulator is included.
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      Fuzzy constrained predictive control of non-linear systems with packet dropouts
      • Author(s): Y. Zhao ; H. Gao ; T. Chen
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1665 –1677
      • DOI:  10.1049/iet-cta.2009.0274
      • Type: Article
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      • p. 1665 –1677 (13)
        This study investigates the problem of fuzzy predictive control of non-linear systems with imperfect communication links. Packet loss (which appears typically in a network environment) is assumed to happen intermittently between the physical plant and the controller, and stochastic variables satisfying the Bernoulli random binary distribution are utilised to describe the imperfect communication phenomenon. The formulation is mathematically transformed into a stochastic Takagi–Sugeno fuzzy model. Attention is focused on the design of fuzzy predictive controllers such that the closed-loop system is stochastically stable, optimising an objective function value at every step in an infinite time horizon subject to input constraints and packet dropouts. A piecewise Lyapunov function approach is utilised, which is effective for fuzzy systems with trapezoidal membership functions; for continuous membership functions, the quadratic Lyapunov function approach is employed. A set of linear matrix inequalities is given to solve the corresponding controller optimisation problem. Two examples are provided to illustrate the usefulness and applicability of the developed theoretical results.
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      On the closed-form model for state covariance assignment problem
      • Author(s): S. Baromand  and  H. Khaloozadeh
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1678 –1686
      • DOI:  10.1049/iet-cta.2009.0546
      • Type: Article
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      • p. 1678 –1686 (9)
        In this study a closed-form innovative scheme for covariance assignment problems based on the original linear stochastic system is proposed. The closed-form of the state covariance equations is derived by converting the covariance matrix Riccati equation to a new linear deterministic vector state space system. As the main result of this study, according to the Kronecker product operator, the closed-form model of the new covariance system matrices is presented. In this study, the authors perform the covariance assignment problem, reformulated as a standard disturbance rejection problem. Since the new covariance system is linear and deterministic, all conventional and well-defined control strategies would be applied.
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      Robust H∞ control and uniformly bounded control for genetic regulatory network with stochastic disturbance
      • Author(s): W. Yu ; J. Lü ; Z.D. Wang ; J. Cao ; Q. Zhou
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1687 –1706
      • DOI:  10.1049/iet-cta.2010.0003
      • Type: Article
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      • p. 1687 –1706 (20)
        Robust H∞ control and uniformly bounded control for a genetic regulatory network (GRN) with stochastic disturbance are considered, where the GRN is delayed with SUM regulatory functions. A sufficient condition is derived to ensure the mean-square stability of stochastic GRN. Robust H∞ controller is then designed to stabilise the stochastic GRN in the mean square sense. Furthermore, some robust uniformly bounded controllers are also proposed to overcome the flaws where H∞ control cannot be used. Finally, numerical results are given to verify the theoretical analysis in this paper.
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      Sensor fault-tolerant vector control of induction motors
      • Author(s): M.E. Romero ; M.M. Seron ; J.A. De Doná
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1707 –1724
      • DOI:  10.1049/iet-cta.2009.0464
      • Type: Article
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      • p. 1707 –1724 (18)
        The authors propose a multisensor switching strategy for fault-tolerant vector control of induction motors. The proposed strategy combines three current sensors and associated observers that estimate the rotor flux. The estimates provided by the observers are compared at each sampling time by a switching mechanism which selects the sensors–observer pair with the smallest error between the estimated flux magnitude and a desired flux reference. The estimates provided by the selected pair are used to implement a vector control law. The authors consider both field-oriented control and direct torque and flux control schemes. Pre-checkable conditions are derived that guarantee fault tolerance under an abrupt fault of a current sensor. These conditions are such that the observers that use measurements from the faulty sensor are automatically avoided by the switching mechanism, thus maintaining good performance levels even in the presence of a faulty sensor. Simulation results under realistic conditions illustrate the effectiveness of the scheme.
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      Model based on the reinitialised partial moments for initialising output-error identification methods
      • Author(s): R. Ouvrard ; E. Tohme ; T. Poinot ; A. Abche
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1725 –1738
      • DOI:  10.1049/iet-cta.2009.0644
      • Type: Article
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      • p. 1725 –1738 (14)
        The present study addresses the initialisation problem of output-error (OE) identification methods. The challenge is to find a suitable initialization, which brings about a convergence towards the global optimum. A common way to initialise OE methods is to use the ARX model, but it must be used cautiously. The purpose of this study is to describe an alternative method based on the reinitialised partial moment (the RPM model) and to compare this approach with the ARX model by analysing the bias. The RPM model property is an implicit embedded filter that substitutes the explicit data filter required by the ARX model.
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      Switching-based emergency braking control for an overhead crane system
      • Author(s): B. Ma ; Y. Fang ; Y. Zhang
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1739 –1747
      • DOI:  10.1049/iet-cta.2009.0277
      • Type: Article
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      • p. 1739 –1747 (9)
        Emergency braking plays an important role in the safety of overhead crane systems; however, it has received little attention so far. Motivated by this fact, two practical guidelines for the emergency braking control of overhead crane systems are proposed, which are safety and efficiency in brief. Based on the guidelines, a novel two-stage switching control strategy is then presented to improve operation safety. Specifically, at the first stage, a braking controller is exerted on the trolley to prevent the payload from moving forward as soon as possible. At the second stage, an energy-based damping controller is adopted to stabilise the overall system rapidly. These two controllers are switched automatically and the switching time is selected carefully to ensure satisfactory control performance. Both simulation and experimental results are presented to demonstrate the effectiveness of the proposed braking control method.
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      Simple disturbance observer for disturbance compensation
      • Author(s): C. Du ; H. Li ; C.K. Thum ; F.L. Lewis ; Y. Wang
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1748 –1755
      • DOI:  10.1049/iet-cta.2009.0178
      • Type: Article
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      • p. 1748 –1755 (8)
        Disturbance observer (DOB) without using additional sensors is an attractive method to attenuate the effects of disturbances as they are highly cost effective. This study proposes a simple form of DOBs, which does not need to solve the plant model inverse, and uses H∞ control method to design the Q-filter in the DOB. The conventional form is proved to be a special case of the proposed form. Comparison to the conventional form of DOBs is made and the significance of the proposed method in DOB design and disturbance attenuation is verified via simulation and experimental results.
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      Model predictive control relevant identification: multiple input multiple output against multiple input single output
      • Author(s): D. Laurı́ ; J.V. Salcedo ; S. Garcı́a-Nieto ; M. Martı́nez
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1756 –1766
      • DOI:  10.1049/iet-cta.2009.0482
      • Type: Article
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      • p. 1756 –1766 (11)
        Model predictive control (MPC) relevant identification (MRI) can be performed by minimising a cost function containing identification errors from multistep ahead predictions. The multiple MISO (multiple input single output) identification approach is often preferred to the MIMO (multiple input multiple output) identification approach in traditional one-step ahead identification. This study aims at comparing the MIMO and multiple MISO identification approaches in MRI. It is argued in this study that, unlike in the one-step ahead approach, MIMO identification is preferable in MRI. As an example, a non-linear MIMO proton exchange membrane fuel cell (PEMFC) is approximated in the neighbourhood of an operating point using the MIMO and MISO approaches.
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      Finite-time stability of linear systems: an approach based on polyhedral Lyapunov functions
      • Author(s): F. Amato ; R. Ambrosino ; M. Ariola ; F. Calabrese
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1767 –1774
      • DOI:  10.1049/iet-cta.2009.0182
      • Type: Article
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      • p. 1767 –1774 (8)
        In this study, the authors consider the finite-time stability (FTS) problem for linear systems. Differently from previous studies, the authors assume that the sets to which the state variables must belong in order to satisfy the FTS requirement are boxes (or more in general polytopes) rather than ellipsoids. To deal with these more realistic constraints on the state variables the stability analysis is performed with the aid of polyhedral Lyapunov functions rather than with the classical quadratic Lyapunov functions. The main result, derived by using polyhedral Lyapunov functions, is a sufficient condition for FTS of linear systems. Detailed analysis and design examples are presented to illustrate the advantages of the proposed methodology over existing methods.
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      Adaptive robust control of uncertain dynamical systems with multiple time-varying delays
      • Author(s): H. Wu
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1775 –1784
      • DOI:  10.1049/iet-cta.2010.0009
      • Type: Article
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      • p. 1775 –1784 (10)
        The problem of adaptive robust stabilisation is considered for a class of dynamical systems with multiple time-varying delayed state perturbations, time-varying uncertain parameters, and external disturbances. It is assumed that the upper bounds of the delayed state perturbations, uncertainties and external disturbances are unknown, and that the time-varying delays are any non-negative continuous and bounded functions. In particular, it is not required that the derivatives of time-varying delays have to be less than one. For such a class of uncertain time-delay systems, a new method is presented whereby a class of memoryless continuous adaptive robust state feedback controllers is proposed. By employing a quasi-Lyapunov function, it is shown that the solutions of uncertain time-delay systems can be guaranteed to be uniformly exponentially convergent towards a ball which can be as small as desired. In addition, since the proposed adaptive robust state feedback controllers are completely independent of time delays, the results obtained in the study may be also applicable to a class of dynamical systems with uncertain time delays. Finally, a numerical example is given to demonstrate the validity of the results.
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      Finite-horizon discrete-time robust guaranteed cost state estimation for non-linear stochastic uncertain systems
      • Author(s): I.R. Petersen
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1785 –1794
      • DOI:  10.1049/iet-cta.2009.0330
      • Type: Article
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      • p. 1785 –1794 (10)
        This study presents a new approach to discrete-time robust non-linear state estimation based on the use of sum quadratic constraints. The approach involves a class of state estimators that include copies on the system non-linearities in the state estimator. The non-linearities being considered are those that satisfy a certain generalised monotonicity condition. The linear part of the state estimator is synthesised using minimax LQG control theory which is closely related to H∞ control theory and this leads to a non-linear state estimator that gives an upper bound on an estimation error cost functional.
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      Hybrid passivity and finite gain stability theorem: stability and control of systems possessing passivity violations
      • Author(s): J.R. Forbes  and  C.J. Damaren
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1795 –1806
      • DOI:  10.1049/iet-cta.2009.0137
      • Type: Article
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      • p. 1795 –1806 (12)
        The stability and control of systems possessing passivity violations is considered. The authors seek to exploit the finite gain characteristics of a plant over a range in which a passive mapping no longer exists while implementing a similar hybrid passive and finite gain controller. Using the dissipative systems framework the authors define a hybrid system: one which possesses a passive map, and finite gain characteristics when the passive map is destroyed. The definition of a hybrid system utilises a switching parameter to break the system into passive and finite gain regions. It is shown that this switching parameter is equivalent to an ideal low-pass filter and can be approximated by a Butterworth filter. The stability of two hybrid systems within a negative feedback interconnection is also considered. A hybrid passivity and finite gain stability theorem is developed using both Lyapunov and input–output techniques, which yield equivalent results. Sufficient conditions for the closed-loop system to be stable are presented, which resemble an amalgamation of the traditional passivity and small-gain theorems.
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      Robustness analysis for a class of linear neutral systems in a critical case
      • Author(s): Q. Quan  and  K.-Y. Cai
      • Source: IET Control Theory & Applications, Volume 4, Issue 9, p. 1807 –1816
      • DOI:  10.1049/iet-cta.2010.0073
      • Type: Article
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      • p. 1807 –1816 (10)
        This study pays attention to robust stability of a class of uncertain neutral systems in a critical case, where the spectral radius of the principal neutral term (matrix H in this study) is equal to 1. It is shown that usual methods cannot deal with such systems with uncertainties. Thus, a novel method is developed, whose idea is to examine whether or not an existing stability criterion still holds when the uncertainties are sufficiently small. More specifically, it is to examine whether or not the existing stability criterion in terms of a linear matrix inequality (LMI) still has a solution with the sufficiently small uncertainties. By analysing the structure of the solution, a new robust stability criterion is derived in terms of the existence of solutions to an equation. An application shows the effectiveness of the proposed method by dealing with a problem caused by numerical methods when solving LMIs.
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