Robust H∞ exponential filtering for uncertain stochastic time-delay systems with Markovian switching and nonlinearities

In this paper, we deal with the robust H∞ exponential filtering problem for a class of uncertain stochastic time-delay systems with Markovian switching and nonlinear disturbances. The system under consideration involves parameter uncertainties, Itoˆ-type stochastic disturbances, Markovian jump parameters, unknown nonlinear disturbances as well as time-varying delays, which vary in a range and dependent on the mode of the operation. The aim of this problem is to design a Markovian jump exponential filter such that the filtering error system is robustly stochastically exponentially mean-square stable, and a prescribed H∞ disturbance attenuation level is guaranteed. Novel delay-range-dependent sufficient conditions are proposed to guarantee the existence of the desired robust exponential filter, which are derived in terms of linear matrix inequalities (LMIs). Then, the explicit expression of the desired filter parameters is characterized. An illustrative numerical example is provided to demonstrate the effectiveness of the proposed method.