Robust exponential stability of impulsive switched systems with switching delays: A Razumikhin approach

In this paper, we focus on the robust exponential stability of a class of uncertain nonlinear impulsive switched systems with switching delays. We introduce a novel type of piecewise Lyapunov–Razumikhin functions. Such functions can efficiently eliminate the impulsive and switching jump of adjacent Lyapunov functions at impulsive switching instants. By Razumikhin technique, the delay-independent criteria of exponential stability are established on the minimum dwell time. Finally, an illustrative numerical example is presented to show the effectiveness of the obtained theoretical results.

► The robust exponential stability problem of the nonlinear impulsive switched systems with switching delays is considered.
► We first introduce a novel piecewise Lyapunov–Razumikhin function.
► Such function can successfully eliminate the impulsive and switching jump phenomenon.
► The robust exponential stability conditions are presented by Lyapunov–Razumikhin method.
► Such conditions are delay-independent and only related to the minimum dwell time.