Robust H∞ Filtering for a Class of Uncertain Nonlinear Stochastic Time-delay Systems

The paper investigates a robust H∞ filtering design problem for a class of uncertain nonlinear stochastic time-delay system with state and exogenous disturbance-dependent noise. Assume the parameter uncertainty is norm-bounded and the system dynamic is modeled by Ito-type stochastic differential equations. The aim of this work is to design a linear, delayless, uncertainties independent state estimator such that for all admissible uncertainties as well as exogenous disturbances, the dynamics of the estimation error is stochastically exponential stable in mean square and independent of the time-delay. Sufficient conditions are proposed to guarantee the existence of desired robust H∞ filtering via linear matrix inequalities (LMI). Numerical example is presented to demonstrate the effectiveness of the proposed approaches.