Integral Input-to-State Stability Of Switched Delay Systems

Switched delay systems as a kind of important and more practical model, are influenced and interacted by time delays, continuous dynamics and discrete dynamic behaviors. Compared with general switched systems or delay systems, switched delay systems are more complicated. The study of switched delay systems is mainly focused on many aspects such as stability, robustness in the field of control theory. Stability is an important and basic property of a system. Delay or disturbance often makes a system unstable, and even if all subsystems are unstable, as long as appropriate switching laws are designed, switched delay systems can eventually achieve stability. There are few results on switched delay systems composed of unstable subsystems, and most of them resort to state-dependent switching strategies, but very few focus on dwell time switching law. Considering the current research status, this paper studies a class of switched delay system, which each subsystem is unstable under dwell time switching. Since switched delay systems with all unstable subsystems are often encountered in practical engineering, stability analysis of such systems is of great prospect and significance.Based on dwell time and Lyapunov theory, input-to-state stability (ISS) and integral input-to-state stability (iISS) of switched delay systems with all unstable subsystems are studied. First, by constructing a multiple Lyapunov functional, the ISS for switched delay systems in nonlinear context is firstly established. By linear interpolation formula, a discretized Lyapunov functional is constructed. Based on linear matrix inequality (LMI) approach, defining the dwell time by a pair of upper and lower bounds, sufficient computable conditions are presented for ISS of linear switched delay systems. A numerical example is given to prove the validity of the results. Next, we consider the less conservative iISS, giving sufficient existence conditions for Lyapunov functional. Since a bilinear system would only achieves iISS instead of ISS, we study a class of bilinear switched delay systems. Through polytope extreme theory, the system is transformed into a more general polytope system. Then a computable sufficient LMI condition is presented with dwell time, which it can ensure the iISS of the bilinear switch delay system. In the end of chapter 3 and chapter 4, a relevant example is given to show the validity of the obtained conclusions.