A Novel Approach to Input-to-State Stability of Impulsive Switched Nonlinear Systems

This paper discusses the input-to-state stability (ISS) of continuous-time impulsive switched nonlinear systems. Based on a novel approach called edge-dependent average dwell time (EDADT), some sufficient conditions are presented to guarantee the ISS of the considered systems containing both ISS and non-ISS subsystems by utilizing Lyapunov functions. It is also shown that when all subsystems are ISS, the systems are ISS under the EDADT scheme even though the switching instants are destabilizing. Conversely, when all subsystems are non-ISS, the designed fast EDADT scheme coupled with stabilizing switchings is sufficient for ISS of the systems. Some generalizations are made compared with the previous ones, which are also illustrated by numerical examples.