Robust H2 and H∞ filter design for uncertain linear systems via LMIs and polynomial matrices

This paper presents new convex optimization procedures for full order robust H2 and H∞ filter design for continuous and discrete-time uncertain linear systems. The time-invariant uncertain parameters are supposed to belong to a polytope with known vertices. Thanks to the use of a larger number of slack variables, linear matrix inequalities for the design of robust filters can be derived from the proposed conditions, outperforming the existing methods. The superiority and efficiency of the proposed method for filter design are illustrated by means of numerical comparisons in benchmark examples from the literature.