Finite-time H∞ control for discrete-time switched systems with admissible edge-dependent average dwell time

This paper is concerned with finite-time ${{H}_{\infty }} $H∞ control for discrete-time switched linear systems via admissible edge-dependent switching. The admissible edge-dependent average dwell-time (AED–ADT) is employed to identify a class of constrained switching signals for the resulting closed-loop system. Moreover, multiple discontinuous Lyapunov function (MDLF) approach, which is less conservative than the traditional multiple Lyapunov function (MLF) method, is used to analyse the closed-loop stability and ${{H}_{\infty }} $H∞ performance by incorporating the idea of AED–ADT. By constructing the MDLFs in quadratic forms, a synthesis condition for finite-time bounded control is first proposed, then a synthesis condition for finite-time ${{H}_{\infty }} $H∞ control is further developed based on the obtained result. Finally, two simulation examples are given to verify the effectiveness and practicability of the presented control synthesis method.