The Stability Analysis And Control For Linear Switched Delay Systems

Due to the reciprocity of dynamic and delay of linear control system, the behavior of switched delay systems is more complicated compared with that of common switched systems or delay systems. The linear switched delay systems have a wide application background and many practical systems can be modeled as switched or hybrid delay systems, such as power systems, networked control systems (NCS) etc. The research on linear switched delay systems has become a hot topic in the international control field in recent years and many results have been achieved. But there are still many urgently solved problems on stability of linear switched delay systems. Based this point, the stability of linear switched delay systems is deeply studed in this dissertation.The problem of exponential stability for a class of linear discrete switched systems is considered first in the Chap.2. The switched systems consist of stable and unstable subsystems. Based on the average dwell time method, we search for some switching signals to guarantee exponential stability of this system. The explicit state decay estimation is also given in the form of the solutions of linear matrix inequalities (LMIs).The problem of non-fragile control for switched linear systems with time-varying delay in detection of switching signal is concerned in the Chap.3. In the case where the controller gain is assumed to have additive gain variations, the design of non-fragile state-feedback controllers is given such that the corresponding closed-loop system is asymptotically stable.The problems of robust fault detection for discrete-time switched systems with state delays and time-varying delay are investigated separately in the Chap.4 and Chap.5. The objective is to design a robust fault detection filter that guarantees both sensitivity to faults and robustness to disturbances. Based on switched Lyapunov functional method, sufficient conditions for the existence of the above filters are given in terms of LMIs.The H∞control problem for a class of NCS based on an even- time-driven mode is considered in the Chap.6, under which, the considered NCS can be changed into a class of switched delay systems including unstable subsystem. The Lyapunov function exponential estimation method is presented to solve the problem of H∞control for such systems. The switching controller is designed to make the considered system exponentially stable with a H∞norm bound in terms of LMIs. It is showed that the obtained results are less conservative than existing ones. Finally, one example is given to illustrate the effectiveness and benefit of the proposed method.