Robust H∞ filtering for uncertain stochastic Markovian jump systems with mode-dependent time delays and nonlinear disturbances
ABSTRACT This paper investigates the problem of robust Hinfin filtering for uncertain nonlinear stochastic time-delay systems with Markovian jump parameters. The system under consideration contains parameter uncertainties, Ito-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 Hinfin disturbance attenuation level is guaranteed. By using the Lyapunov stability theory and Ito 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 Hinfin 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.