Stability Analysis And Controller Design For Switched Delayed Systems

The switched system is a very special class of hybrid systems. The dynamicbehavior of the switched system is more complex than other systems, due to not onlyuncertainty and also time delay. More importantly, switching behavior interact withuncertainty and time delay, which makes the system very complex. Therefore, about theswitching system, a lot of analysis and synthesis problem to be solved.It is well known stability analysis is a basis of the study of kinetics. In chapter2,This article first discusses the relationship between switching rules and stability, giventhat because of the existence of a switching rule, there is no positive correlation betweenthe stability of the switched systems and its subsystems stability. Later, we carry out abrief introduction about switched systems stability analysis approaches, providing atheoretical basis for the subsequent stability analysis.In chapter3, we analyze the stability of the time-varying delay switched systemand switched systems with constant delay. We propose the average dwell time approachand piecewise Lyapunov function technique, which we will use later.In chapter4, our study is concerned with theL₂L_∞control problem forcontinuous-time switched systems with time-varying delay. A dynamic output feedback（DOF） controller is designed, which is assumed to be switching with the same switchingsignal as in the original system. By using an average dwell time approach and thepiecewise Lyapunov function technique, a delay-dependent sufficient condition isproposed to guarantee the exponential stability and a weightedL₂L_∞performancefor the closed-loop system with the decay estimate explicitly given. The correspondingsolvability condition for a desired DOF controller is established, and an explicitparametrisation of all desired DOF controllers is also given. Finally, we have anumerical example to prove the effectiveness of the proposed theories.Chapter5is concerned with H_∞model reduction for continuous-time linearswitched systems with time-varying delay. For a given stable switched system, ourattention is focused on construction of a reduced-order model such that the error systemis exponentially stable with a prescribed weighted H_∞performance. By applying theaverage dwell time approach and the piecewise Lyapunov function technique,deley-independent sufficient conditions are proposed in terms of linear matrix inequality（LMI） to guarantee the exponential stability and the weighted H_∞performance for theerror system. The model reduction problem is solved by using the projection approach, which casts the model reduction problem into a sequential minimization problemsubject to LMI constraints by employing the cone complementary linearizationalgorithm. A numerical example is provided to illustrate the effectiveness of theproposed theory.