Robust filtering for uncertain linear descriptor systems

This paper is concerned with the problem of robust filtering for uncertain linear descriptor systems. The matrices of the system state-space model are uncertain, belonging to a given polytope. A method based on a parameter-dependent Lyapunov function is proposed for designing a linear stationary filter that ensures an optimized upper-bound on the asymptotic error variance, irrespective of the parameter uncertainty. The proposed design is given in terms of linear matrix inequalities which depend on a scalar parameter that should be searched for in order to optimize the filter performance.