This study focuses on the robust -stability analysis of fractional order interval systems (FOISes). The concept of interval means that the coefficients of the systems transfer functions are uncertain parameters that each adopts a value in a real interval. Initially, some new bounds on the poles of the FOISes are produced so that they reduce the computational burden in the case of the -stability. Then, the concept of the value set is extended to analyse the robust -stability of the FOISes, and a new necessary and sufficient condition is presented. The value set of the FOISes is obtained analytically, and based on it an auxiliary function is introduced to check the condition. The obtained results are applicable to systems of both commensurate and incommensurate orders. Moreover, it is perceived that if a family of a FOIS is of commensurate order, then the robust -stability can be checked by checking the -stability of a finite number of family members, i.e. a generalisation of Kharitonov's theorem. Finally, the presented theorems are applied to the control system of a space tether system.

A vector-valued model-based cumulative sum (CUSUM) procedure is proposed for identifying faulty/falsified sensor measurements. First, given the system dynamics, the authors derive tools for tuning the CUSUM procedure in the fault/attack-free case to fulfil the desired detection performance (in terms of false alarm rate). They use the widely-used chi-squared fault/attack detection procedure as a benchmark to compare the performance of the CUSUM. In particular, they characterise the state degradation that a class of attacks can induce the system while enforcing that the detectors (CUSUM and chi-squared) do not raise alarms. In doing so, they find the upper bound of state degradation that is possible by an undetected attacker. They quantify the advantage of using a dynamic detector (CUSUM), which leverages the history of the state, over a static detector (chi-squared), which uses a single measurement at a time. Simulations of a chemical reactor with a heat exchanger are presented to illustrate the performance of their tools.

Iterative learning control (ILC) is an effective approach for tracking control system that performs repeating tasks. However, the performance of ILC is significantly deteriorated when the reference is changed. To obtain high tracking performance for both repeating and varying tasks, a novel data-driven tuning method of feedforward controller structured with infinite impulse response (IIR) filter via ILC is developed in this study. Global optimal parameters of the feedforward controller are obtained by linear least-squares method based on the optimal feedforward control force obtained by ILC, while model information is not required. Additionally, to deal with the possible instability problem of the feedforward controller structured with IIR filter, a stable approximation approach on the basis of zero-phase-error tracking algorithm is presented. The stable approximation approach can convert the approximation problem to a convex optimisation problem. Finally, the proposed approach is compared with the standard ILC and a data-driven feedforward control structured with finite impulse response filter by two simulation studies. Simulation results demonstrate that the proposed data-driven feedforward tuning method can achieve high tracking performance and is insensitive to reference variations.

In this study, a simultaneous local stabilisation and fault detection (FD) problem for Takagi-Sugeno (T-S) fuzzy systems is investigated. The authors' attention is focused on synthesising an FD observer and an observer-based controller to achieve the objectives of local stabilisation and FD simultaneously. First, by establishing the relationship among the reachable set, the ellipsoid set and the objective area, a new local stabilisation criterion is proposed. The presented criterion guarantees that the state trajectory starting from a given local region can remain in this region even when the system is subject to disturbances and faults. Meanwhile, the FD observer is designed under a mixed framework such that the residual signal is robust to the persistent disturbance and sensitive to the fault. Different from some existing methods, via the proposed scheme, the state can be restricted into the modelling area so that the non-linear control problem can be addressed by the T-S fuzzy model approach effectively. Additionally, two different methods are utilised in the co-design of the observer and the controller such that the disturbance is not required to be energy-bounded. Finally, the effectiveness of the proposed approach is demonstrated by an example.

In this study, the problem of output consensus control for high-order continuous-time linear multi-agent systems with interval time-varying delays is investigated. The observability decomposition technique is employed to design the output consensus protocols which are the collections of delayed output information from neighbouring agents. On the basis of invertible transformations, output consensus for the concerned dynamical agents is transformed into the problem of asymptotical stability analysis for some lower dimensional subsystems. By introducing the prescribed convergence rate scalar into the constructed delay-dependent Lyapunov functionals, the framework for output consensus analysis is theoretically derived. Benefitting from the method of slack matrix variables, sufficient conditions are obtained in terms of linear matrix inequalities to design the protocol gain matrices which can guarantee the property of output consensus. Moreover, the output consensus function determined merely by the initial states of dynamic agents and consensus protocol is presented without the influences of time-varying delays. Numerical examples are exploited to illustrate the effectiveness of the derived results.

This study addresses the design of static output feedback (SOF) controller for continuous time linear systems. New sufficient conditions are derived for designing SOF controllers. The development involves suitable decomposition of Lyapunov matrices and deriving linear matrix inequality (LMI) criterion that ensures performance. LMI criteria for pole placement in the LMI region are also derived. The proposed criteria can be used for restricted SOF controller design effectively. Several numerical examples are presented to demonstrate the effectiveness of the proposed results.

Distributed containment control of multi-agent systems with asynchronous switching and stochastic disturbances under a time-invariant directed graph is studied. Since both the process of identifying an active subsystem and that of applying a matched controller to the corresponding subsystem need to consume time, the controller switching usually lags behind the subsystem switching. In order to show that the controllers are still effective to tolerate some time delay, a multiple Lyapunov function is selected to present stability conditions. By employing stochastic stabilisation theory and matrix transformation, the problem of containment control is transformed to that of stability analysis of the closed-loop system and exponential stabilisation in mean square sense is achieved. Finally, two simulation examples are given to verify the effectiveness of the proposed results.

In a modern thermal power plant, fuzzy model predictive control (MPC) is an effective method for realising load tracking and economy of boiler–turbine system, by using fuzzy modelling technique considering the plant thermal dynamic. The power plant economy is generally handled in a hierarchical MPC (HMPC) architecture, in which the upper layer realises the economic optimisation while the low layer realises the dynamic tracking. However, while this HMPC architecture realises the steady-state optimisation, it may neglect the dynamic optimum of the total power plant process. This study develops a fuzzy economic MPC to utilise the economic index directly as the cost function. It integrates economic optimisation and dynamic tracking of the boiler–turbine system control into one framework. Since a fuzzy model is used to approximate the system's non-linear behaviour, a linear feedback controller can be constituted for guaranteeing the feasibility and stability of the boiler–turbine system through linear matrix inequality. Simulation results are given to show the effectiveness of the proposed controller.

An adaptive multivariable continuous non-singular terminal sliding mode (NTSM) control scheme with fast and robust input shaper (FRIS) is developed for flexible spacecraft which is subject to external disturbances. Firstly, the FRIS is proposed to suppress residual vibration of flexible spacecraft. It is shown that the FRIS decreases the duration of the impulse sequence at the meanwhile it is robust to parameter uncertainties. Then the adaptive multivariable continuous NTSM control is proposed to the attitude tracking of flexible spacecraft and the supression of residual vibration in finite time. The remarkable feature of the developed algorithm is to eliminate the overestimation of the control gains, and the tracking errors can be driven into a small region around zero in finite time even in the presence of bounded but unknown disturbances. Finally, some numerical simulations are performed to validate the efficiency of the developed algorithm.

This study focuses on the problem of time-delayed impulsive control with actuator saturation for discrete-time dynamical systems. By establishing a delayed-impulsive difference inequality, combining with convex analysis and inequality techniques, some sufficient conditions are obtained to ensure exponential stability for discrete-time dynamical systems via time-delayed impulsive controller with actuator saturation. And those results are also used in the problem of synchronisation of the discrete-time complex networks. The designed controller admits the existence of some transmission delays in impulsive feedback law, and the control input variables are required to stay within an availability zone. Several numerical simulations are also given to demonstrate the effectiveness of the proposed results.

This mainly studies the mean square stabilisability, interval stability and stabilisation of mean-field stochastic control systems. A necessary and sufficient condition for stabilisation of continuous-time mean-field stochastic systems is presented via operator spectrum technique. The unremovable spectrum is generalised to mean-field stochastic differential equations (MF-SDEs), and a necessary and sufficient condition for unremovable spectrum is obtained. Three operators defined in different domains are given to characterise the stabilisability of MF-SDEs. As applications, an example is given to illustrate their relationships. Interval stability and stabilisation are generalised to MF-SDEs, and a necessary condition for interval stability is given to show the relationship among interval stability, the decay rate of the system state response and the Lyapunov exponent. A sufficient condition for interval stabilisation is proposed via linear matrix inequality approach.

In this study, the authors consider the state estimation problem for a class of non-linear systems with unknown time-varying delays. Based on the filtering method, they propose a new observer design approach where the states of the non-linear systems with unknown delays can be robustly estimated. While relevant results in the literature assume the unknown delays to be differentiable, the observer design proposed in this study only requires the knowledge of the unknown delays' upper and lower bounds which can be obtained in practical systems. The new observer design approach also allows us to consider delays in the output measurements. They further utilise the linear parameter varying approach to relax the conservativeness imposed on observer design conditions by the Lipschitz conditions. To show the effectiveness of the new results, the single-link joint robotic system and the pendulum system are considered as illustrative examples.

This study considers structure preserving balanced proper orthogonal decomposition for second-order form systems via shifted Legendre polynomials. The proposed approach is to use time interval empirical Gramians of the first-order representation, which are constructed from impulse responses by solving block tridiagonal linear systems, to generate approximate balanced system for the large-scale second-order form system. The balancing transformation is directly computed from the expansion coefficients of impulse responses in the space spanned by shifted Legendre polynomials, without computing the full Gramians for the first-order representation. Then, the reduced second-order model is constructed by truncating the states corresponding to the small approximate singular values. Furthermore, in combination with the dominant subspace projection method, the authors modify the reduction procedure to alleviate the shortcoming of the above method, which may unexpectedly lead to unstable systems even though the original one is stable. The stability preservation of the reduced model is briefly discussed. Finally, the effectiveness of the proposed methods is demonstrated by two numerical experiments.

This work studies the demand-side management problem and intermittent control for a class of networked smart grids. Firstly, the networked smart grid is modelled into a special networked evolutionary game via the semi-tensor product of matrices. Secondly, to minimise the overall cost of all the communities and reduce the control execution time, intermittent control is designed for some communities, in which these players work as controllers at some special strategy profiles. By designing the intermittent open-loop control, a necessary and sufficient condition is provided to assure the stabilisation of the networked smart grid. Then, an intermittent state feedback control is designed, based on which, the smart grid can converge to the desired strategy profile globally. Algorithms that can compute the state feedback controllers are given. Finally, a numerical example is worked out to illustrate the effectiveness of the developed theoretical results.

In this study, a fixed point iteration-based subspace identification method is proposed for Hammerstein state-space systems. The original system is decomposed into two subsystems with fewer parameters based on the hierarchical identification principle. Each subsystem is related directly to either the linear dynamics or the static non-linearity. A two-stage least-squares-based iterative method is then implemented to separately estimate the coefficients of the non-linear subsystem and the extended Markov parameters of the linear subsystem. The linear subsystem parameters are extracted from the identified extended Markov parameters using a singular value decomposition based method. Convergence analysis of the proposed method is established using fixed point theory, which shows that the proposed method gives consistent estimates under arbitrary non-zero initial conditions. Simulation results are included to show the performance of the proposed method.

In this work, the authors investigate event-triggered stabilisation problem for continuous-time switched systems, where switching instants and transitions are under given constraints. By designing some event-triggered conditions and a proper switching law, they establish some sufficient stabilisation criteria for the considered systems. The proposed event-triggered scheme is advantageous to reduce the utilisation of communication and computation resources. Further, they study the switching synchronisation problem for two continuous-time switched non-linear systems with different initial values. Finally, an example of Chua's circuit with simulations results are presented to illustrate the validity of the method.

The problem of composite adaptive disturbance observer-based control and weighted performance analysis for a class switched stochastic systems with multiple disturbances subject to mode-dependent average dwell time switching are studied. A disturbance observer and an adaptive updated law are constructed to further design a state feedback controller. Some sufficient criteria are established to check the stability of the switched stochastic systems with multiple disturbances in terms of the multiple Lyapunov function technique. Furthermore, a composite adaptive disturbance observer based-controller is also given. Finally, two examples are proposed to prove the validity of the obtained results.

The main objective of this work is to propose a method for the data-driven evaluation of fault diagnosability in dynamic systems. This technique promises to be an efficient way to analyse the structural properties of unknown systems and can be used to optimise a system configuration, including sensor placement. The basic idea behind this method, which suitably integrates direct identification methods into the fault diagnosability evaluation, lies in the invariability of the characteristics of the dynamic behaviour corresponding to different fault cases. Data-driven realisations of distinguishability based on both fault-free data and fault data are proposed. Furthermore, a novel efficient method for computing distinguishability via the pseudoinverse is proposed. Finally, the effectiveness of the proposed method is illustrated via numerical and practical examples.

This study investigates the quantised-input FIR (finite impulse response) system identification under quantised and event-triggered output observations. For the binary-valued quantisation, they introduce a so-called either–or communication scheme to save communication resources. Based on the received data and the triggered indicator, an identification algorithm is proposed to estimate the unknown parameter by use of the empirical measure and weighted least squares. The convergence performance is established and the communication rate is derived. For the multi-threshold quantisation, it can be seen as a vector-valued observation in which each component represents a binary-valued output, and the corresponding identification problem is discussed. A numerical example is included to illustrate the main results obtained.

The authors consider the problem of multi-player evolutionary game with two strategies and an arbitrary number of players. A randomised probabilistic access model is considered where the users randomly select the strategies. The strategies are a selection between two radio access technologies to receive service from. For a fair resource allocation between a number of users, the payoff function of each player is considered to be inversely proportional to the number of players choosing a strategy. It is valid for the radio access technology selection problem where resources are divided fairly between the users. The necessary and sufficient conditions for the existence and uniqueness of a mixed Nash equilibrium point of the game is provided. In addition, it is proved that the mixed Nash equilibrium point of the game is globally asymptotically stable and also evolutionarily stable strategy.