Robust H<inf>∞</inf> filter design for uncertain singular stochastic systems

Abstract

This paper deals with the problem of robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filter design for uncertain singular stochastic systems. Based on linear matrix inequalities (LMIS) techniques and stability theory of stochastic differential equations, stochastic Lyapunov function method is adopted to design a H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filter such that, for all admissible uncertainties, the filtering error system is stochastically mean-square stable, and a prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> disturbance attenuation level is guaranteed. A sufficient condition for the existence of a H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filter for the system under consideration is achieved in terms of LMIS. Moreover, the explicit expression of the desired filter parameters is given.