Robust generalized H2 filtering for uncertain discrete-time linear systems

This paper considers the problem of robust generalized H₂ filtering for discrete-time linear systems with polytopic uncertainties. Based on parameter-dependent Lyapunov functions combined with Finsler's lemma, new conditions for the solvability of the problem are given in terms of linear matrix inequalities (LMIs). Compared to the existing results, more slack variables are introduced to provide extra freedom for the generalized H₂ optimization which lead to improving the performance and reducing the conservatism further. An example is give to illustrate the effectiveness of the proposed method.