Robust H∞ filtering for uncertain stochastic Markovian jump systems with mode-dependent time delays and nonlinear disturbances

This paper investigates the problem of robust H∞ filtering for 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 Markovian jump linear filter such that, for all admissible uncertainties, nonlinearities and time-delays, the filtering error system is robustly asymptotically mean-square stable, and a prescribed H∞ disturbance attenuation level is guaranteed. By using the Lyapunov stability theory and Itô differential rule, some novel delay-range-dependent sufficient conditions in terms of linear matrix inequality (LMI) are proposed to guarantee the existence of the desired H∞ filter. Then, the explicit expression of the desired filter parameters is characterized. An illustrative numerical example is provided to demonstrate the effectiveness and applicability of the proposed method.