Finite-time asynchronous control of linear time-varying switched systems

In the framework of asynchronous control, finite-time stabilization and finite-time bounded stabilization of linear time-varying (LTV) switched systems are investigated. A necessary and sufficient condition for finite-time stability (FTS) of LTV switched systems is proposed based on differential matrix inequalities (DMIs). Moreover, we extend the FTS result to the case of finite-time boundedness (FTB), and present a sufficient condition of FTB for LTV switched systems using the average dwell time method which can be used for design proposes. Then we turn to the design problem of asynchronously switched control to guarantee FTS or FTB of LTV switched systems and give a sufficient condition for the state feedback stabilization in the form of nonlinear DMIs (NDMIs). A numerical method is proposed to solve NDMIs approximately. Finally, two examples are given to illustrate the validity of the results.