Robust L2 – L∞ filter design for stochastic systems

This paper discusses robust L₂ - L_∞ filter design for a class of stochastic systems with time-varying delay. The aim is to design a full order filter such that the error system is asymptotically mean-square stable and a prescribed level γ is satisfied. Both filter analysis and synthesis problems are considered. To reduce the conservatism of the results, the time delay varies in an interval [h₁,h₂] and a novel inequality is given. Then, based on the novel LKF and inequality, some new delay-dependent conditions for the existence of robust L₂ - L_∞ filter are presented in terms of linear matrix inequalities. Finally, numerical examples show the effectiveness of the proposed method.