Robust $H_{\infty }$ Filtering for Nonlinear Discrete-time Stochastic Systems

Abstract

This paper mainly discusses the $H_{\infty }$ filtering of general nonlinear discrete time-varying stochastic systems. A nonlinear discrete-time stochastic bounded real lemma (SBRL) is firstly obtained by means of the smoothness of the conditional mathematical expectation, and then, based on the given SBRL and a stochastic LaSalle-type theorem, a sufficient condition for the existence of the $H_{\infty }$ filtering of general nonlinear discrete time-varying stochastic systems is presented via a new introduced Hamilton-Jacobi inequality (HJI), which is easily verified. When the worst-case disturbance $\{v_k^{\ast }{\}}_{k\in \mathcal{N}}$ is considered, the suboptimal $H_2/H_{\infty }$ filtering is studied. Two examples including a practical engineering example show the effectiveness of our main results.