Robust full- and reduced-order energy-to-peak filtering for discrete-time uncertain linear systems

The problem of robust energy-to-peak filtering for uncertain discrete-time systems is revisited in this paper. The considered uncertain parameters of system matrices are supposed to reside in a polytope and the attention is focused on the design of robust full- and reduced-order filters guaranteeing a prescribed energy-to-peak noise-attenuation level for all admissible uncertainties. By making full use of the Finsler lemma associated with Projection lemma, two further improved energy-to-peak filtering methods are obtained, where more auxiliary slack variables are introduced to provide extra free degrees. Then, the filters can be readily designed by solving a set of less conservative linear matrix inequalities (LMIs). Finally, two examples are given to illustrate the effectiveness of the proposed approaches.