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.

Robust mixed H2 and passive switching control for uncertain discrete switched systems with time delay

In this paper, the problem of mixed ${H}_2$ and passive switching control of uncertain discrete time-delay switched systems is investigated via a switching signal selection. Lyapunov theory with Wirtinger inequality is applied to guarantee the mixed performance for discrete switched time-delay system. The used Linear Matrix Inequality variables are less than our past proposed results. Finally, the improvement of the developed results is illustrated via a numerical example.