New Stability and Stabilization Conditions of Switched Systems with Mode-Dependent Average Dwell Time

In this paper, the problems of stability and stabilization for switched systems with mode-dependent average dwell time (MDADT) switching are revisited and discussed in both continuous-time and discrete-time contexts. By introducing a class of quasi-alternative switching signals, some improved stability conditions of switched systems with MDADT are obtained. In our switching design strategy, slow switching and fast switching are, respectively, used among stable subsystems and unstable subsystems. Then, based on the stability result, stabilization conditions for switched linear systems comprising uncontrollable subsystems are presented to guarantee the underlying system to be exponentially stable. The criteria obtained for the considered switched linear systems are all provided in terms of a set of linear matrix inequalities. To illustrate the advantages of our established results, a numerical example is finally given.