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The Luenberger observer technique has long been used for reliable state estimation of feedback control systems. In this paper it is employed for asynchronously switched control systems. The theory of finite-time stability (FTS) and finite-time boundedness (FTB) is incorporated, which is a relatively new concept offering open and challenging problems, especially in the field of robust state estimation for switched control systems. Many real-world systems are supposed to run for a fixed interval of time and hence the design of finite-time state observers has more significance from the point of view of many engineering applications. This investigation considers asynchronous switching between observer and physical systems, which accounts for inherent delays in practical applications caused by measurement and sensing mechanisms, and crafts a more practical and accurate design method. Furthermore, H∞ performance index which is a vital technique for robust system design against external disturbances is integrated in the design procedure.

SUMMARY In this paper, the control synthesis problem for a class of large-scale systems with multi-modes that are called large-scale switched systems is addressed. By introducing the concept of decentralized switching signal and the relevant decentralized average dwell time, the asymptotic stability and weighted l2 gain performance are investigated. It should be noted that the decentralized switching covers general switching cases for large-scale switched systems, namely, it admits both time-dependent switching signal and arbitrary switching signal blended in the decentralized switching. Then, on the basis of the analysis results, the decentralized weighted control scheme including state feedback controller gains and switching signals is studied. Several design algorithms are proposed to meet different controller design problems. Finally, numerical examples are provided to illustrate theoretical findings within this paper. Copyright © 2013 John Wiley & Sons, Ltd.

SUMMARY In this note, the state estimation problem for a class of short-time switched linear systems is investigated. By incorporating the concept of finite-time stability, an observer is designed to ensure the error dynamics finite-time stable in the short-time switching interval under the general asynchronous switching whereas synchronous switching mode is its special case. A numerical example is provided to illustrate the effectiveness of our study in this paper. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, a new approach for stability analysis of time-dependent switched linear systems is proposed. System equivalence is the main idea in this new approach, which derives a switched discrete linear parameter-varying system from the switched continuous-time linear switched system with interval dwell time, and the stability properties of the two corresponding systems are proved to be equivalent. Then, by applying a quadratic Lyapunov function approach for the equivalent switched discrete system, the stability of the switched continuous-time linear system can be established without checking any average dwell time condition. Finally the computation complexity is analyzed, and mode incidence matrix is introduced to reduce the computation cost.

SUMMARY Because switched system with nonlinear subsystems shows great difficulties in controller design by conventional methodologies, the fuzzy logic theory, which has been proven to be a practical and effective way to deal with the analysis and synthesis problems for complex nonlinear systems, is applied to design a class of hybrid fuzzy controller for switched discrete-time fuzzy system in this paper. On a basis of one step prediction of switching signal, a hybrid parallel distributed compensation (PDC) control strategy is proposed, which includes two necessary parts: the state feedback controllers for subsystems and the update feedback controllers for switching instants. In both arbitrary and dwell-time switching cases investigated, it is proved that the hybrid PDC controller contains less conservativeness than conventional switched PDC controller. Numerical examples are given to illustrate the effectiveness and advantages of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.

SUMMARY In this paper, several concepts of switching frequency are introduced to analyze the properties and performance of switched systems in infinite as well as finite-time intervals. The observation is very motivating that different system properties and performances depend on different switching frequencies. Sufficient conditions ensuring asymptotic stability, l2 gain performance, and state boundness are derived on the basis of the notions of switching frequency, respectively. Then, on the basis of the analysis results, the control synthesis problems are addressed. LMI-based design algorithms are proposed to meet different control synthesis requirements. Numerical design examples are provided to demonstrate our results. Copyright © 2011 John Wiley & Sons, Ltd.

SUMMARY In this paper, we investigate the stability analysis problem of switched impulsive nonlinear systems and several stabilization problems of switched discrete-time linear systems are studied. First, sufficient conditions ensuring globally uniformly asymptotically stability of switched nonlinear impulsive system under arbitrary and DDT (dynamical dwell time which defines the length of the time interval between two successive switchings) switching are derived, respectively. In the DDT switching case, we first consider the switched system composed by stable subsystems, then we extend the results to the case where not all subsystems are stable. The stabilizations of switched discrete-time linear system under arbitrary switching, DDT switching and asynchronous switching are investigated respectively. Based on the stability analysis results, the control synthesis consists of controller design for each subsystem and state impulsive jumping generators design at switching instant. With the aid of the state impulsive jumping generators at switching instant, the ‘energy’ produced by switching can be minimized, which leads to less conservative results. Several numerical examples are given to illustrate the proposed results within this paper. Copyright © 2011 John Wiley & Sons, Ltd.