Finite-time H∞ control of discrete-time switched systems based on transferring-dependent Lyapunov function approach

Abstract

This paper studies the finite-time issues (finite-time stability, finite-time boundedness, finite-time [Formula: see text] control) of discrete-time switched systems. Different from the existing Lyapunov function (LF) approaches only concerning activated subsystem, a novel approach for constructing LF is first proposed, which not only depends on the subsystem the switching reaches but also is closely related to the freshly inactive subsystem. Based on this, a transferring-dependent convex Lyapunov function (CLF) and a transferring-dependent LF are introduced, under which the improved finite-time stability results are deduced with admissible edge-dependent average dwell time (AED-ADT) technique. In light of the merits of established finite-time stability criteria, two transferring-dependent controllers are devised—that is, transferring-dependent convex controller (TD-CC) and transferring-dependent ordinary controller (TD-OC)—to perform finite-time control synthesis. Then, the finite-time [Formula: see text] control is further investigated based on the obtained control synthesis results. The designed transferring–dependent controllers can guarantee that the underlying system is finite-time bounded (FTB) with a prescribed [Formula: see text] performance under tighter AED-ADT switching signals. Besides, it is the first time to use the multiple convex Lyapunov function (MCLF) to investigate the finite-time issues. Finally, two numerical examples and a practical example are used to verify the effectiveness of the developed results.