Stability analysis of switching systems under the improved persistent dwell time strategy

Abstract

For discrete-time switching systems, the new concept of $\Phi$-dependent average persistent dwell time ($\Phi$APDT) is proposed for the first time. Based on the $\Phi$APDT strategy and the quasi-time-varying Lyapunov function approach, global exponential stability conditions for discrete-time switching systems in linear and nonlinear cases are derived. Then, using linear matrix inequalities, the relevant results can be applied to the design of stabilizing controllers for discrete-time switching linear systems. Finally, a typical numerical example is used to compare the $\Phi$APDT strategy with PDT and MDPDT strategies to confirm the effectiveness and superiority of the new strategy.