Robust H ∞ filtering for uncertain discrete-time descriptor systems

Abstract

This paper considers the robust H ∞ filtering problem for uncertain discrete-time descriptor systems. A class of uncertain systems with norm-bounded uncertainties is considered. The necessary and sufficient condition for solvability of the robust full-order H ∞ filtering is introduced which is generally less conservative than those existing sufficient conditions only. Explicit expressions of these filters are given. In addition to the full-order filtering problem, the robust reduced-order H ∞ filtering is also addressed by using slack variables technique in new sufficient conditions. The parameters of reduced-order filters are directly extracted from the solvability conditions. All the above conditions are convex and are expressed in term of linear matrix inequalities (LMIs) by using the original system matrices. The results generalize the previously developed H ∞ filter design for standard discretetime systems. A numerical example is presented to demonstrate the effectiveness of the proposed approaches.