A Lyapunov-like functional approach to stability for impulsive systems with polytopic uncertainties

This paper is concerned with a Lyapunov-like functional approach to stability for impulsive systems with polytopic uncertainties. At first, a Lyapunov-like functional approach is established to investigate the stability for impulsive systems, with the Lyapunov-like functional dependent on time explicitly, discontinuous, and not imposed to be definite positive. A specific Lyapunov-like functional is created by introducing the integral of the system state and the cross terms among this integral and the impulsive state. To estimate the derivative of the functional, a new inequality is proposed, and an integral equation of the impulsive system is employed. By the Lyapunov-like functional theory, a new asymptotical stability result is obtained for impulsive systems without uncertainties. Then, the stability result is further extended to impulsive systems with polytopic uncertainties. At last, some numerical examples are given to illustrate that the proposed stability results have less conservatism than some existing ones.