Stability of Time-Varying Impulsive Systems With State-Dependent Delay and Its Application in Complex Networks.

Abstract

This study investigates the stability of a set of time-varying impulsive systems incorporating state-dependent delay (SDD). The coexistence of SDD, time-varying parameters, and impulsive effects introduces strong nonlinear coupling between the system trajectory and the delay term, which makes the analysis more challenging than that of constant or time-varying delay systems. In terms of Lyapunov, several sufficient conditions are developed to guarantee the stability of the considered systems. The proposed criteria reveal the interaction mechanism among continuous dynamics, impulsive disturbances, and SDD, thereby characterizing the inherent robustness against impulsive perturbations. Furthermore, the derived results are extended to the synchronization problem of complex networks with impulsive disturbances. Two examples are provided to verify the validity and applicability of the derived results.