Input-to-state stability via hybrid time approach applied in Hybrid dynamical systems with time-delay

In this paper, by using the concept of hybrid time for Hybrid dynamical systems (HDS), we consider the problem of input-to-state stability (ISS) for a class of nonlinear HDS with interval time-varying delay and external inputs. Some sufficient conditions are presented aiming to derive the ISS and exponential ISS properties of the whole hybrid systems for the case in which the continuous subsystem and discrete subsystem of the hybrid dynamical systems have no ISS properties. These interval time of continuous subsystem and discrete subsystem demonstrate that contribute to the exponential ISS property for the time delay hybrid system. Finally, some examples are given for illustration.