H_∞ Filtering And Fault Detection Of Switched Delay Systems

Switched delay systems are an important class of hybrid systems, whose applications can be widely found in engineering. Due to the interaction among the continuous-time (discrete-time) dynamics, discrete event states and the existence of time delays, the dy-namic behavior of switched delay systems is very complicated. Mechanism of system evolution is not clear and many problems of analysis and synthesis of such systems re-quire to be studied. This dissertation is concerned with the problems of H∞filter design and fault detection of switched delay systems. The main contributions are as follows.The problem of H∞filter design for discrete-time switched systems with state delays is investigated. Based on a novel linearization technique, sufficient conditions for the ex-istence of filters are obtained, by solving which a desired filter can be constructed. The problem of robust fault detection for discrete-time switched systems with state delays under an arbitrary switching signal is studied. The fault detection filter is used as the residual generator. Attention is focused on designing the robust fault detection filter such that, for unknown inputs, control inputs, and model uncertainties, the estimation error between the residuals and faults is minimized. Utilizing H∞theory, the problem of robust fault detection is converted into an H∞-filtering problem. By a switched Lyapunov func-tional approach, a sufficient condition for the solvability of this problem is established. The problem of delay-dependent H∞filter design for a class of discrete-time switched systems with state delays is studied. By using switched Lyapunov function method and free-weighting matrix method, choosing a new Lyapunov function and utilizing lineariza-tion technique, delay-dependent sufficient conditions on the existence of a desired filter are presented.The problem of delay-dependent exponential H∞filtering for discrete-time switched delay systems is investigated under average dwell time (ADT) switching signals. By intro-ducing a proper factor to construct a novel Lyapunov function and using ADT approach, sufficient conditions for the solvability of this problem are obtained. The switching signals with average dwell times are given. It is proved in theory that the proposed Lyapunov function is less conservative and more general than the existing one.The problem of exponential H∞filtering for a class of continue-time switched system with interval time-varying delays is studied. Based on the free weighting matrix approach and average dwell time technology, delay-dependent sufficient conditions for the existence of such filter are derived. The robust fault detection problem for continuous-time switched systems with state delays is addressed. The fault detection filter is used as the residual generator. Attention is focused on designing the filter such that, for the modeling errors, the unknown inputs and the control one, the error between the residuals and the faults is minimized. The addressed fault detection filter design is converted into an auxiliary H∞filtering problem. By using the Lyapunov-Krasovskii functional method and average dwell time approach, a sufficient condition for the solvability of this problem is established.Delay-dependent exponential stability criteria are presented for switched systems consisting of a family of stable and unstable subsystems with an interval time-varying delay. By introducing some free-weighting matrices, constructing the new Lyapunov-Krasovskii functional and taking advantage of average dwell time technique, sufficient conditions for such criteria are obtained. The problem of controller failure analysis for a class of interval time-varying delay systems by a pre-designed state feedback controller is transformed into the stability problem of switched delay systems with stable and unstable subsystems. Based on piecewise Lyapunov functional method, sufficient conditions for the exponential stability of such systems are presented.The problems of delay-dependent exponential H∞model reduction for discrete-time and continuous-time switched delay systems are considered, respectively. The objective is to construct the reduced-order models to approach the original models in the H∞sense. By making use of ADT approach and introducing a new block matrix to decouple, the restriction of the non-convex constraints of traditional method is overcome and delay-dependent sufficient conditions for the existence of reduced-order models are derived in terms of strict LMIs. Compared to the existing method, the heavy calculation is reduced.