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Dissipative Control of Two-Dimensional Switched Fornasini-Marchesini Systems

This paper investigates the dissipativity-based stability analysis and control problems for the two-dimensional (2-D) switched Fornasini-Marchesini (FM) systems. Firstly, the definition of 2-D (T, S, R)-δ-dissipativity is introduced for the FM systems. Next, the sufficient condition to guarantee the asymptotical stability and 2-D (T, S, R)-δ-dissipativity of the switched FM systems is proposed. Then based on the obtained dissipative stability condition, the 2-D (T, S, R)-δ-dissipative state-feedback controller is designed via the projection lemma technique. Finally, the effectiveness of the proposed 2-D (T, S, R)-δ-dissipative controller design method is illustrated by a numerical example.