Finite frequency $$H_\infty $$H∞ control of 2-D continuous systems in Roesser model

This paper investigates the finite frequency (FF) $$H_\infty $$H∞ 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 $$H_\infty $$H∞ 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 $$H_\infty $$H∞ controllers are obtained in terms of linear matrix inequalities. Two examples are given to validate the proposed methods.

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