Input‐to‐state stability of nonlinear stochastic time‐varying systems with impulsive effects
Xiaotai Wu, Peng Jia Shi, Yang Shan Tang, Wenbing Zhang · International Journal of Robust and Nonlinear Control · 2016
Summary This paper considers the input‐to‐state stability, integral‐ISS, and stochastic‐ISS for impulsive nonlinear stochastic systems. The Lyapunov function considered in this paper is indefinite, that is, the rate coefficient of the Lyapunov function is time‐varying, which can be positive or negative along time evolution. Lyapunov‐based sufficient conditions are established for ensuring ISS of impulsive nonlinear stochastic systems. Three examples involving one from networked control systems are provided to illustrate the effectiveness of theoretical results obtained. Copyright © 2016 John Wiley & Sons, Ltd.