Robustness Analysis of Global Exponential Stability of Nonlinear Systems With Deviating Argument and Stochastic Disturbance

Abstract

Robust performance of nonlinear systems has attracted phenomenal worldwide attention. It is well known that deviating argument and stochastic disturbance may derail the evolution properties of nonlinear systems. Then the following issue has become a major bottleneck: for a given globally exponentially stable nonlinear system, the perturbed nonlinear system can sustain how much the length of the interval of the deviating function and the noise intensity so that the perturbed nonlinear system in the presence of deviating argument and stochastic disturbance may remain to be exponentially stable. In this paper, theoretical investigation has been made on the robustness of global exponential stability of nonlinear systems with deviating argument and stochastic disturbance. The allowable upper bounds of the length of interval of deviating function and the noise intensity are derived for the perturbed nonlinear systems to remain exponentially stable. It is also proven that, if the length of interval of deviating function and the noise intensity of perturbed nonlinear systems are lower than the upper bounds derived herein, the nonlinear systems infected by deviating argument and stochastic disturbance are still exponentially stable. Finally, we give several simulation examples to demonstrate the efficacy of the proposed results.