Input-to-state stability of discrete-time time-varying impulsive delay systems

This paper investigates the input-to-state stability (ISS) of nonlinear discrete-time time-varying impulsive delay systems with the coexistence of stabilising and destabilising impulses. Some ISS criteria are established for discrete-time impulsive delay systems by employing the Lyapunov functional where the coefficient of the estimated upper bound of the time difference of the Lyapunov functional is allowed to be a time-varying function which can take both negative and positive values. In addition, the ISS of a class of discrete-time linear time-varying impulsive delay systems is discussed by utilising a non-quadratic Lyapunov functional. Numerical examples are presented to verify the effectiveness of the main results.

Automated summary

This paper investigates the input-to-state stability (ISS) of nonlinear discrete-time time-varying impulsive delay systems with the coexistence of stabilising and destabilising impulses. The ISS criteria for discrete-time impulsive delay systems are established using the Lyapunov functional, where the coefficient of the estimated upper bound of the time difference of the Lyapunov functional can be a time-varying function. The ISS of a class of discrete-time linear time-varying impulsive delay systems is also discussed by utilizing a non-quadratic Lyapunov functional. Numerical examples are presented to verify the effectiveness of the main results.