Input-to-state stability of nonlinear systems with hybrid inputs and delayed impulses

This paper addresses input-to-state stability (ISS) and integral input-to-state stability (iISS) problem of impulsive systems with hybrid inputs and delayed impulses. By adopting Lyapunov function method, sufficient conditions for ISS/iISS are established, and the impact of time delay in hybrid impulses, that is, the stabilizing impulses and destabilizing impulses, are further studied. Moreover, several examples are given and numerical simulations are performed to illustrate their usefulness.