Robust stability criteria for linear impulsive delay systems

Abstract

AbstractThis article is concerned with robust stability for linear impulsive delay systems with polytope uncertainties. For the linear impulsive delay systems without uncertainties, the stability is addressed by employing a Lyapunov‐Krasovskii‐like functional, which is comprised of a Lyapunov‐Krasovskii functional and an auxiliary functional. By introducing integrals of the state, an augmented Lyapunov‐Krasovskii‐like functional is constructed. With an integral inequality proposed to deal with the derivative of the Lyapunov‐Krasovskii‐like functional, a stability criterion is derived for the impulsive delay system. Then the stability criterion is extended to linear impulsive delay systems with polytope uncertainties, and a robust stability criterion is obtained. Examples are given to illustrate the stability results are valid or of less conservatism than some existing ones.