Stability and L₂–Gain analysis of linear switched singular systems by using multiple discontinuous Lyapunov function approach

In this paper, the problem of the E-exponential stability and $l_2-\mathrm{gain}$ analysis of linear switched singular systems is investigated in discrete-time case. By using a multiple discontinuous Lyapunov function approach and adopting the mode-dependent average dwell time (MDADT) switching signals, new sufficient conditions of E-exponential stability and $l_2-\mathrm{gain}$ analysis for linear switched singular systems are presented. Based on the above results, we also derive the weighted $l_2-\mathrm{gain}$ performance index. In addition, by utilizing our proposed method, tighter bounds on average dwell time can be obtained for our considered systems. At last, a numerical example is given to show the effectiveness of the results.