H∞ exponential filtering for uncertain Markovian jump stochastic systems with mode-dependent time delays and nonlinearities

This paper investigates the problem of delay-range-dependent robust H_∞ exponential filter design for uncertain stochastic delayed systems with Markovian switching and nonlinear disturbances. The system under consideration involves Markovian jump parameters, parameter uncertainties, Ito-type stochastic disturbances, nonlinearities 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 linear filter such that, for all admissible uncertainties, 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 exponential filter, which are derived in terms of linear matrix inequalities (LMIs). Also, the explicit expression of the desired filter parameters is given. An illustrative numerical example is provided to demonstrate the effectiveness and usefulness of the proposed method.