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Finite frequency $$H_\infty$$ control of 2-D continuous systems in Roesser model. (English) Zbl 1381.93038
Summary: This paper investigates the Finite Frequency (FF) $$H_\infty$$ control problem of two-dimensional (2-D) continuous systems in Roesser Model. Our attention is focused on designing state feedback controllers guaranteeing the bounded-input-bounded-output stability and FF $$H_\infty$$ performance of the corresponding closed-loop system. A generalized 2-D Kalman-Yakubovich-Popov (KYP) lemma is presented for 2-D continuous systems. By the generalized 2-D KYP lemma, the existence conditions of $$H_\infty$$ controllers are obtained in terms of linear matrix inequalities. Two examples are given to validate the proposed methods.

##### MSC:
 93B36 $$H^\infty$$-control 93B52 Feedback control 93C05 Linear systems in control theory 93C20 Control/observation systems governed by partial differential equations
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