New noise‐to‐state stability and instability criteria for random nonlinear systems

Abstract

SummaryThis paper investigates the noise‐to‐state stability and instability criteria for random nonlinear affine systems. Firstly, some new noise‐to‐state stability theorems, which weaken the sufficient conditions in the existing stability criteria on random nonlinear systems, are given by means of the uniformly asymptotically stable function. Secondly, the noise‐to‐state instability definitions are introduced and the sufficient conditions of noise‐to‐state instability are provided based on a new established lemma and the uniformly asymptotically stable function. Finally, some examples show the feasibility of theoretical findings.