Research On Stability Of Linear Switched Systems

Switched systems are one kind of the important classes of hybrid systems, which consist of a family of subsystems and switching sequence. Based on the switching sequence the switched system achieves the expected performance. This dissertation mainly discusses the stability of linear switched systems. In the course of research the questions that the asymptotic stability of continuous switched systems and discrete switched systems with arbitrary switching sequence and period switching sequence are focused.Research the asymptotic stability of linear automatic switched systems, and a necessary and sufficient condition for the asymptotic stability of linear automatic switched systems with equal-time interval switching sequences is obtained. Then extend the above conclusion and research to the problem of stability of automatic switched systems with period switching sequences. Put forward a method that constructing the period switching sequence for a class of automatic switched systems.Focus on the stability of linear discrete switched systems; bring forward the condition of asymptotic stability of linear discrete automatic switched systems with arbitrary switching sequence and period switching sequence.Extend the research area from automatic switched systems to switched systems with control vectors. Research the asymptotic stability of continuous switched systems with control vectors based on period switching sequence. Then introduce uncertainty disturbance and put forward a necessary and sufficient condition for state feedback stability of continuous switched systems with period switching sequence and using the LMI to solve the problem that stabling the switched systems with period switching sequence.Research the question of the stability of discrete switched systems with control vectors based on arbitrary switching sequence and period switching sequence. Provide the concrete design method for the state feedback controller for discrete switched system with period switching sequence.