Delay-dependent robust H∞ filtering for linear stochastic systems with uncertainties

This paper investigates the robustH∞ filtering problem for continuous –time linear stochastic systems with time-vary state delay and parameter uncertainty. The aim is to design a linear filter such that the filtering error dynamics system is exponentially stable in mean square and assuring a prescribedH∞ performance level .Applying the descriptor model transformation, construct a new Lyapunov-Krasovskii functional . By introducing some free weighting matrices, avoiding any product term of Lyapunov matrices and system matrices，so it is not necessary for system matrices to do any constraint in the process of the design of filters, to a great extent , which make the design of filters have less conservative. For system without uncertainty and with uncertainty case, to guarantee the existence of desired robust H∞ filters, sufficient conditions are proposed respectively in terms of linear matrix inequalities (LMIs), The results obtained are less conservative than existing ones. Numerical examples demonstrate the proposed approaches are effective and are an improvement over previous ones.