Online ISSN
1751-8652
Print ISSN
1751-8644
IET Control Theory & Applications
Volume 3, Issue 8, August 2009
Volumes & issues:
Volume 3, Issue 8
August 2009
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- Author(s): B. Zhou ; Z.-Y. Li ; G.-R. Duan ; Y. Wang
- Source: IET Control Theory & Applications, Volume 3, Issue 8, p. 983 –994
- DOI: 10.1049/iet-cta.2007.0371
- Type: Article
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p.
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This study is concerned with designing a feedback gain to minimise a quadratic performance index with guaranteed pole locations for closed-loop discrete-time linear systems. Firstly, a method that shifts the open-loop poles to desired locations by using a parametric linear Stein equation is presented. Then a recursive approach is proposed to shift every eigenvalue of a discrete-time linear system separately without mode decomposition in each step. By using such method, it is required to solve a linear Stein matrix equation of low order in each step. The presented method yields a solution which is optimal with respect to a quadratic performance index that can be obtained explicitly. The attractive feature of this method comparing with existing results is that it enables solutions to complex problems to be easily found without solving any non-linear algebraic Riccati equations. Moreover, analytical solutions can be obtained which may have advantages in some design problems. Numerical examples illustrate the proposed approach. - Author(s): L. Li and Y. Jia
- Source: IET Control Theory & Applications, Volume 3, Issue 8, p. 995 –1005
- DOI: 10.1049/iet-cta.2008.0008
- Type: Article
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995
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This paper is devoted to the problems of non-fragile H∞ and L2–L∞ control for a class of linear systems with time-varying state delay. The purpose is to design a dynamic output feedback controller with additive gain variations such that the closed-loop system is asymptotically stable while satisfying a prescribed H∞ (or L2–L∞) performance level. By using linear matrix inequality approach, a delay-dependent stability criterion is obtained by introducing a new type of Lyapunov–Krasovskii functional. Based on the obtained criterion, sufficient conditions for the existence of desired controllers are derived, and the corresponding stabilisation dynamic output feedback controller design algorithm is proposed. Numerical examples are included to illustrate the benefit and effectiveness of the proposed method. - Author(s): K. Hu and J. Yuan
- Source: IET Control Theory & Applications, Volume 3, Issue 8, p. 1006 –1016
- DOI: 10.1049/iet-cta.2008.0122
- Type: Article
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1006
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This study deals with the problem of H∞ output-feedback control for switched linear discrete-time systems with time-varying delay. A delay-dependent stability criterion for a given H∞ performance is derived by employing finite sum equality based on quadratic terms, a new method of estimating the upper bound on the finite sum. Both static and dynamic H∞ output-feedback controllers are designed based on a performance analysis. Moreover, a modified cone complementary linearisation algorithm is exploited to solve the non-convex feasibility problem. Numerical examples are given to illustrate the theoretical results. - Author(s): K. Subbarao and P.C. Muralidhar
- Source: IET Control Theory & Applications, Volume 3, Issue 8, p. 1017 –1022
- DOI: 10.1049/iet-cta.2008.0012
- Type: Article
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1017
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This paper analyses the stability properties of a state observer estimating the system states from delayed measurements for a linear time invariant plant. The delay is assumed to be a known piecewise constant function of time. The observer construction is a two-step procedure and has a ‘chain-like’ structure, consisting of two cascaded dynamical systems. The manifestation of the time-varying delayed output on the observer stability is analysed at both the ‘zeroth’ and the ‘first’ links in the chain of observers. - Author(s): J. Fu
- Source: IET Control Theory & Applications, Volume 3, Issue 8, p. 1023 –1032
- DOI: 10.1049/iet-cta.2008.0117
- Type: Article
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1023
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In this study, an extended backstepping approach is developed for tracking control of a class of systems that are globally diffeomorphic into systems in generalised output feedback canonical form. Output-dependent non-linearities are allowed to enter such a system both additively and multiplicatively. The system contains unknown parameters multiplied by output-dependent non-linearities. This method relies on a parameter estimator and state observer design and standard backstepping construction. Compared with the traditional parameter estimation and state observation, the approach in this study has three distinct features due to adopting the new adaptive mechanism recently developed in literature. First, the parameter estimator and state observer does not follow the classical certainty equivalent principle. Second, the design treats the unknown parameter estimation and unmeasured state observation in a united way. Third, unlike the conventional observer-based backstepping, the design does not require the construction of Lyapunov function for every augmented sub-system. Furthermore, the method is applied to the stabilisation of single-machine-infinite-bus power systems with steam valve control using only measurements of the power angle as an illustrative example. A typical example is also given to show that the proposed method can be applied to more general systems which violate the cascading upper diagonal dominance conditions. - Author(s): Y.G. Sun ; L. Wang ; G. Xie
- Source: IET Control Theory & Applications, Volume 3, Issue 8, p. 1033 –1040
- DOI: 10.1049/iet-cta.2008.0162
- Type: Article
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1033
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By using the average dwell time approach, we identify a class of switching signals to guarantee exponential stability and L2 gain of the switched linear system with interval time-varying delay excluding zero. By taking both the lower bound and upper bound of delay into consideration in the chosen Lyapunov function, several new stability criteria are presented in terms of linear matrix inequalities. Compared with some results in the literature, it is theoretically established that our results are less restrictive. - Author(s): Z.R. Xiang and R.H. Wang
- Source: IET Control Theory & Applications, Volume 3, Issue 8, p. 1041 –1050
- DOI: 10.1049/iet-cta.2008.0150
- Type: Article
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The problem of robust control for uncertain switched non-linear systems with time delay under asynchronous switching is investigated. Firstly, when there exists asynchronous switching between the controller and the system, a sufficient condition for the existence of stabilising switching law for time-delay switched system is derived. Then, the proposed approach is extended to design stabilising controller and switching law for switched non-linear systems with time delay under asynchronous switching. Furthermore, the problem of robust control for uncertain switched non-linear systems with time delay under asynchronous switching is also investigated. Finally, a numerical example is given to illustrate the effectiveness of the proposed method. - Author(s): H.-B. Shi and L. Qi
- Source: IET Control Theory & Applications, Volume 3, Issue 8, p. 1051 –1058
- DOI: 10.1049/iet-cta.2008.0185
- Type: Article
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p.
1051
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This study deals with simultaneous stabilisation of linear time-invariant systems via static output feedback by designing transformations of state vectors that contain free variables. The transformations reformulate each system as two interconnected systems, and one of the isolated subsystem is stabilised by choosing the free variable as a style of state feedback. Then the common feedback gain matrix can be determined if a linear matrix inequality system is feasible. This method does not concern any reduction or enlargement of matrix inequalities, and is effective for non-minimum phase systems. Numerical examples show the validity of the proposed algorithms for both continuous and discrete systems. - Author(s): H. Zhang ; G. Feng ; C. Dang
- Source: IET Control Theory & Applications, Volume 3, Issue 8, p. 1059 –1069
- DOI: 10.1049/iet-cta.2008.0200
- Type: Article
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The problem of the stochastic stability and H∞ control for uncertain stochastic piecewise-linear systems is studied. The stability analysis is based on Lyapunov functions that are continuous and piecewise quadratic. It is shown that the stability in the mean square for uncertain stochastic piecewise-linear systems can be established if a piecewise quadratic Lyapunov function can be constructed, and moreover, the function can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. It is also demonstrated via a numerical example that the stability result based on the piecewise quadratic Lyapunov functions is less conservative than that based on the common quadratic Lyapunov functions. The H∞ controllers can also be designed by solving a set of bilinear matrix inequalities (BMIs) based on the powerful piecewise quadratic Lyapunov function. - Author(s): D.W. Kim ; J.B. Park ; Y.H. Joo
- Source: IET Control Theory & Applications, Volume 3, Issue 8, p. 1070 –1080
- DOI: 10.1049/iet-cta.2008.0133
- Type: Article
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This study addresses a new digital redesign (DR) problem for a linear time-invariant (LTI) system with a perturbation that is an uncertain non-linear time-varying function but linearly bounded. Given a continuous-time linear controller robustly stabilising the origin of the perturbed system for all admissible perturbations, the concerned DR problem is to design the sampled-data linear controller making trajectories of the continuous-time and the sampled-data non-linear control systems close, or at least robustly stabilising the perturbed system. The proposed approach interprets the DR problem as the stabilisation problem considering the convergence rate for error dynamics between the continuous-time and the sampled-data non-linear control systems. Sufficient conditions for the stabilisation are derived and formulated in the form of linear matrix inequalities (LMIs). A numerical example is used to demonstrate the effectiveness of the proposed design technique. - Author(s): M. Zerar ; F. Cazaurang ; A. Zolghadri
- Source: IET Control Theory & Applications, Volume 3, Issue 8, p. 1081 –1092
- DOI: 10.1049/iet-cta.2008.0057
- Type: Article
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p.
1081
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An linear parameter varying guidance method for the hypersonic phase of a space re-entry vehicle is presented. The suggested guidance scheme, relying on flatness approach, is applied to the non-linear model of the European Atmospheric Re-entry Demonstrator. It is shown that the overall guidance scheme achieves robust stability and performance, even in the presence of entry point kinematics dispersions. The design problem is formulated and solved using a finite set of linear matrix inequalities. Finally, Monte Carlo simulation results are presented to demonstrate the effectiveness of the suggested approach. - Author(s): H.K. Lam and S.C. Tan
- Source: IET Control Theory & Applications, Volume 3, Issue 8, p. 1093 –1106
- DOI: 10.1049/iet-cta.2008.0168
- Type: Article
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This study presents a non-linear design methodology for fuzzy controllers employed in switching DC–DC converters that operates in large-signal domain. Unlike conventional controller design approach, which addresses only the small-signal system stability, the proposed design methodology tackles the design using a non-linear control viewpoint. The proposed approach uses a Tagaki–Sugeno (T–S) fuzzy model to represent the switching converter. The Lyapunov theory is then adopted to derive the sufficient stability conditions in terms of linear matrix inequalities. These inequalities are then employed for the design of a large-signal stable fuzzy controller. Worth mentioning is that the consideration of the circuit parameter uncertainty and the mismatch of the fuzzy membership functions in the proposed approach, greatly complicate the stability analysis, which leads to a conservative result. To alleviate the conservativeness, a membership-function condition is proposed to guide the design of the membership functions of the fuzzy controller. Furthermore, free matrices can be introduced to further relax the conservativeness of stability analysis result. Simulation results on the regulation of a boost DC–DC converter subject to load and input voltage disturbances, using the proposed fuzzy controller are provided to illustrate the effectiveness of the proposed approach. - Author(s): M.S. Mahmoud and A.Y. Al-Rayyah
- Source: IET Control Theory & Applications, Volume 3, Issue 8, p. 1107 –1118
- DOI: 10.1049/iet-cta.2008.0152
- Type: Article
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In this study, we provide efficient solution to the problems of delay-dependent analysis and feedback synthesis for a class of linear continuous-time systems with time-varying delays. An augmented Lyapunov functional is properly constructed and an improved free-weighting method is deployed to exhibit the delay-dependent dynamics. Delay-dependent stability analysis is then performed to develop linear matrix inequalities (LMIs)-based conditions under which the linear delay system is asymptotically stable with an γ-level ℒ2 gain. The superiority of the developed method in comparison with other existing methods is established. By delay-dependent feedback synthesis, we design state-feedback and dynamic output-feedback schemes to guarantee that the closed-loop system enjoys the delay-dependent asymptotic stability with a prescribed γ-level ℒ2 gain. Extension to systems with convex-bounded parameter uncertainties in all system matrices is also provided. All the developed results are tested on representative examples. - Author(s): D.F. Coutinho ; L.F.A. Pereira ; T. Yoneyama
- Source: IET Control Theory & Applications, Volume 3, Issue 8, p. 1119 –1131
- DOI: 10.1049/iet-cta.2007.0411
- Type: Article
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This study addresses the problem of designing compensators for robust model matching. Firstly, the open-loop reference model (obtained, for instance, from classical frequency domain specifications), Gm(s), is recast as the product between two transfer functions GR(s) and Gr(s). A robust state feedback control law is synthesised such that an upper-bound on the ℋ2-norm of the error system between the uncertain system and Gr(s) is minimised, where the state feedback gain is determined through a convex optimisation problem over linear matrix inequality constraints. In addition, block GR(s) behaves as a series compensator in a unity feedback strategy aiming a robust steady state performance. A robust observer scheme is also proposed whenever the states are not available online to the state feedback controller. Numerical examples are presented to illustrate the approach. - Author(s): Y. Gao ; Z. Liu ; H. Chen
- Source: IET Control Theory & Applications, Volume 3, Issue 8, p. 1132 –1144
- DOI: 10.1049/iet-cta.2008.0182
- Type: Article
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In this study, a novel robust H∞ control scheme is presented for discrete-time piecewise affine (PWA) systems in the presence of time-varying uncertainties, external disturbance and time-domain constraints. The suggested control method is formulated as linear matrix inequalities (LMIs), and solved much more efficiently than current methods which could be only cast as bilinear matrix inequalities (BMIs). The key ideas are to introduce a parameter-dependent piecewise-quadratic Lyapunov function (PDPWQLF) to guarantee the closed-loop system to be energy dissipative, and use the concept of approximating polytopic operating regions by ellipsoids. The resulting controller can guarantee robust closed-loop properties, including stability, H∞ performance and the satisfaction of constraints. An example is presented to verify the proposed theoretical results. - Author(s): C.-F. Lin ; W.-C. Su ; K.-H. Liu
- Source: IET Control Theory & Applications, Volume 3, Issue 8, p. 1145 –1154
- DOI: 10.1049/iet-cta.2008.0116
- Type: Article
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This study presents a dynamic post-filtering approach to a single-input-single-output sampled-data variable structure output feedback control problem. Given a sliding surface, Σ(x)=0 (x being the system state vector), designed through standard procedures with the assumption of full state accessibility, a dynamic filter, denoted post-filter, is employed to synthesise Σ(x) by means of output variable alone. In contrast with a state observer, the post-filter is invariant of the matched disturbances; and it requires only partial information of the system parameters. Thus, the robustness property of the variable structure system is retained. Let T be the sampling period. A sampled-data realisation of the post-filter is done by zero-order hold. Depending on the system relative degree, either Σk or Σk−1 can be obtained for implementing the variable structure control law. A discrete-time switching-type control law, which is originally designed to satisfy the continuous-time reaching condition, will lead to a quasi-sliding motion, forming a boundary layer of thickness O(T) about the sliding surface. The stability of the post-filter is ensured if the system output is in minimum phase and that the sliding mode dynamics are chosen properly.
Optimal pole assignment for discrete-time systems via Stein equations
Non-fragile dynamic output feedback control for linear systems with time-varying delay
Finite sum equality approach to H∞ output-feedback control for switched linear discrete-time systems with time-varying delay
State observer for linear systems with piece-wise constant output delays
Extended backstepping approach for a class of non-linear systems in generalised output feedback canonical form
Exponential stability of switched systems with interval time-varying delay
Robust control for uncertain switched non-linear systems with time delay under asynchronous switching
Static output feedback simultaneous stabilisation via coordinates transformations with free variables
Stability analysis and H∞ control for uncertain stochastic piecewise-linear systems
Robust stabilisation of sampled-data control systems with non-linear perturbations via digital redesign
Coupled linear parameter varying and flatness-based approach for space re-entry vehicles guidance
Stability analysis of fuzzy-model-based control systems: application on regulation of switching DC–DC converter
Efficient parameterisation to stability and feedback synthesis of linear time-delay systems
Robust ℋ2 model matching from frequency domain specifications
Robust H∞ control for constrained discrete-time piecewise affine systems with time-varying parametric uncertainties
Post-filtering approach to output feedback variable structure control for single-input-single-output sampled-data systems
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