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In this paper, the analysis on stability and -gain is presented for switched systemswith unstable modes. To solve the problem, an improved mode-dependent average dwell time (MDADT) tradeoff switching method is developed by a time subsequence technique. Based on a general multiple discontinuous Lyapunov functions (MDLFs), stability conditions are acquired for switched nonlinear systems with unstable modes. Whereafter, the stability result is extended to the weighted -gain analysis for the system with external disturbance. Moreover, in light of the quadratic MDLFs, the stability and weighted -gain criteria are also presented for the liner systems under the obtained switching scheme. Due to the time subsequence technique, the proposed switching method is more convenient in practice. Particularly, under the switching scheme, the tighter bounds are provided for MDADT, and the MDADT on unstable modes is not restricted by upper bounds. Finally, numerical examples show that the proposed methods are effective.

Stability and ℒ 2 -gain analysis based on multiple discontinuous Lyapunov function approaches for switched systems with unstable modes