Abstract
In this paper, we deal with H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> filtering problem for a class of two-dimensional (2-D) discrete time-invariant systems with state delays described by local state-space (LSS) Fornasini-Marchesini (FM) second model. Based on the bounded real lemma of 2-D state-delayed systems, H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> filtering design is developed, such that the filtering error system is asymptotically stable and has H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> performance γ via LMIs’ feasibility. Furthermore, the minimum H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> norm bound γ can be obtained by solving a linear objective optimization problem. A numerical example is given to demonstrate the effectiveness and advantage of our result.
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