Input-to-state stability of time-varying nonlinear discrete-time systems via indefinite difference Lyapunov functions

In this paper, we propose new sufficient criteria for input-to-state stability (ISS) of time-varying nonlinear discrete-time systems via indefinite difference Lyapunov functions. The proposed sufficient conditions for ISS of system are more relaxed than for ISS with respect to Lyapunov functions with negative definite difference. We prove system is ISS by two methods. The first way is to prove system is ISS by indefinite difference ISS Lyapunov functions. The second method is to prove system is ISS via introducing an auxiliary system and indefinite difference robust Lyapunov functions. The comparison of the sufficient conditions for ISS obtained via the two methods is discussed. The effectiveness of our results is illustrated by three numerical examples.