Improved stability results for discrete-time switched systems: A multiple piecewise convex Lyapunov function approach

Abstract In this paper, the stability problem is investigated for a class of discrete-time switched systems with unstable subsystems under the mode-dependent average dwell time (MDADT) switching. A multiple convex Lyapunov function (MCLF) and a multiple piecewise convex Lyapunov function (MPCLF) are firstly proposed, which are formulated in a convex combination form of positive definite matrices with quasi-time-dependent coefficients. It is pointed out in the paper that the multiple Lyapunov function (MLF) and the multiple discontinuous Lyapunov function (MDLF) can be regarded as special cases of the proposed MCLF and MPCLF, respectively. Then, the exponential stability conditions are derived by the new Lyapunov functions. Both slow switching and fast switching are exerted on stable modes and unstable modes, respectively. Finally, two numerical examples are given to demonstrate that larger stability regions and tighter MDADT bounds can be obtained by using our developed techniques compared with some recent results.