Finite frequency \(H_\infty \) control of 2-D continuous systems in Roesser model.

*(English)*Zbl 1381.93038Summary: 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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\textit{Z. Duan} and \textit{Z. Xiang}, Multidimensional Syst. Signal Process. 28, No. 4, 1481--1497 (2017; Zbl 1381.93038)

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