Hybrid control of impulsive systems with distributed delays

This paper investigates the stabilization of a class of nonlinear systems with distributed delays using impulsive control and switching control. Stabilizing impulsive forces as well as destabilizing disturbance impulses are considered. Verifiable sufficient conditions are established which guarantee the asymptotic or exponential stability of switched and impulsive systems with distributed delays. Results are found for when the impulses are applied at pre-specified times or at the switching instances. The criteria found are based on a special type of state-dependent switching rule which partitions the state space into stabilizing subregions. The main results are proved using a common Lyapunov functional.