H ∞ Filtering for two-dimensional discrete switched systems in the second Fornasini and Marchesini model

This paper is concerned with the H_∞ filtering problem for two-dimensional (2-D) discrete switched systems described by the second Fornasini and Marchesini (FM) model. The main purpose is to design a switched filter such that the resulting filtering error system under the arbitrary switching signal is asymptotically stable with a guaranteed H_∞ performance level. By using the switched Lyapunov functions, a new sufficient condition is obtained to guarantee the asymptotic stability with a H_∞ performance index for the filtering error system. Based on this condition, the full- and reduced-order H_∞ filter design conditions are derived and formulated in terms of linear matrix inequalities (LMIs). Two illustrative examples are utilized to show the effectiveness and less conservativeness of the proposed method.