ℋ∞andl₂–l∞filtering for two‐dimensional linear parameter‐varying systems

In this paper, the ℋ︁ ∞ and l 2 – l ∞ filtering problem is investigated for two‐dimensional (2‐D) discrete‐time linear parameter‐varying (LPV) systems. Based on the well‐known Fornasini–Marchesini local state‐space (FMLSS) model, the mathematical model of 2‐D systems under consideration is established by incorporating the parameter‐varying phenomenon. The purpose of the problem addressed is to design full‐order ℋ︁ ∞ and l 2 – l ∞ filters such that the filtering error dynamics is asymptotic stable and the prescribed noise attenuation levels in ℋ︁ ∞ and l 2 – l ∞ senses can be achieved, respectively. Sufficient conditions are derived for existence of such filters in terms of parameterized linear matrix inequalities (PLMIs), and the corresponding filter synthesis problem is then transformed into a convex optimization problem that can be efficiently solved by using standard software packages. A simulation example is exploited to demonstrate the usefulness and effectiveness of the proposed design method.