Stability Analysis For Switched Delay Systems

Switched delay systems, a new type of complex systems, find many applications in engineering and have great significance of theoretical study. Due to the interaction among the continuous dynamics and discrete dynamics and time delays, the behavior of such systems is very complicated. Mechanism of system evolution is not clear and many problems of analysis and syntheses need to be studied. This dissertation studies stability of switched delay systems and the main contributions are as follows.An average dwell time method is introduced into linear switched delay systems for the first time. Based on this method, the problem of robust exponential stability of linear switched delay systems is discussed, in which delays are constants. Conditions in the form of linear matrix inequalities (LMIs) are presented to guarantee robust exponential stability of such systems with exponential decay estimates for the states explicitly developed.The problems of exponential stability and L₂ gain for a class of switched delay systems with time-varying delay are studied. The derivative of delays can be arbitrary large. Based on average dwell time method, we search for a class of switching signals such that the considered switched delay systems are exponentially stable and have weighted L₂ -gain. Sufficient conditions in the form of LMIs are given to guarantee the existence for such switching signals. Moreover, state decay estimates are also presented. As a special case, the results on exponential stability and normal L₂ -gain underarbitrary switching are obtained.Exponential stability for switched delay systems consisting of stable and unstable subsystems is addressed. Under the condition that activation time ratio between stable subsystems and unstable ones is not less than a specified constant, sufficient conditions are given to guarantee exponential stability of the switched delay systems. Subsequently, for a special class of switched delay systems, a lower bound on the average dwell time and the activation time ratio of subsystems are calculated respectively by solving a set of linear matrix inequalities (LMIs) and certain equations.The concept of switched neutral delay systems is introduced. Asymptotical stability...