Exponential stability of discrete-time switched systems based on a switched time-varying Lyapunov function

This article investigates some new exponential stability criteria of discrete-time switched systems with both disturbance and impulse. By introducing a novel multiple switched time-varying matrix function, sufficient conditions are presented to ensure the discrete-time switched system to be exponentially stable and achieve $H_{\infty}$ performance under the mode-dependent interval dwell-time switching. Eventually, two numerical examples with unstable subsystems are presented which verify the validity of our conclusions.