Robust H∞ Filtering for Uncertain Nonlinear Stochastic Systems with Mode-dependent Time-delays and Markovian Jump Parameters

This paper investigates the problem of robust H∞ filtering for a class of uncertain nonlinear stochastic time-delay systems with Markovian jump parameters. The system under consideration contains parameter uncertainties, Itô-type stochastic disturbances, unknown nonlinearities as well as time-varying delays, which vary in a range and dependent on the mode of the operation. We aim to design a full-order Markovian jump filter such that, for all admissible uncertainties, the filtering error system is robustly asymptotically stable in the mean square, and a prescribed H∞ disturbance attenuation level is guaranteed. By using the Lyapunov stability theory and Itô differential rule, some sufficient conditions in terms of linear matrix inequality (LMI) are proposed to guarantee the existence of the desired H∞ filter. Then, the explicit expressions of the desired filter parameters are given. Illustrative examples are provided to demonstrate the effectiveness and applicability of the proposed method.