Robust H∞ filtering for linear descriptor systems with convex bounded uncertainty

This paper is concerned with the problem of robust H_∞ 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 with a prescribed H_∞ performance, 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.