Dissipativity and dwell time specifications of switched discrete-time systems and its applications in H∞H∞ and robust passive control

In this paper, the dissipativity and dwell time specifications of switched discrete-time system are investigated. In general case, the dissipativity and the desirable induced Lyapunov stability of switched systems can be established by imposing non-increasing condition on multiple storage functions at switching instants. Then, a novel dwell-time dependent storage function (DTDSF) is introduced to characterize non-increasing condition in linear case, and a corresponding LMI-based sufficient condition is proposed for the dissipativity. Since the derived conditions are all convex in system matrices, it is very convenient to be applied into controller design. As applications, the H∞H∞ and robust passive control problem are considered. Particularly, a solution is proposed for the open problem on the computation of ℓ2ℓ2-induced gains versus dwell time, which is covered by the control problems in this paper. Based on the DTDSF approach, the control synthesis procedures including both controller and switching law design are unified into a one-step method which explicitly facilitates the control synthesis process. Finally, several numerical examples are provided to illustrate our theoretic findings.