Path-Wise Bounds and iISS of Nonlinear Systems Exposed to Global Stochastic Noise * *The work was supported in part by JSPS KAKENHI Grant Number 26420422.

Abstract

Abstract This paper peruses path-wise bounds, integral input-to-state stability and integral noise-to-state stability for stochastic nonlinear systems and proposes their Lyapunov-type characterizations. The characterizations are utilized to develop small-gain criteria to verify stability of interconnected systems. In contrast to preceding results, the developments allow stochastic noise to be active globally in the state space. The obtained criteria are made parallel to deterministic ones by resolving fundamental issues arising from stochastic noises.