Robust [formula omitted] filtering for nonlinear discrete-time stochastic systems

Abstract

This paper mainly discusses the H∞ filtering of general nonlinear discrete time-varying stochastic systems. A nonlinear discrete-time stochastic bounded real lemma is firstly obtained by means of the smoothness of the conditional mathematical expectation, and then, based on the given stochastic bounded real lemma and a stochastic LaSalle-type theorem, a sufficient condition for the existence of the H∞ filtering of general nonlinear discrete time-varying stochastic systems is presented via a newly introduced Hamilton–Jacobi inequality (HJI), which is easily verified. When the worst-case disturbance {vk∗}k∈N is considered, the suboptimal H2∕H∞ filtering is studied. Three examples including a practical engineering example show the effectiveness of our main results.