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

This 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.