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Robust H∞ control for uncertain 2D state-delayed systems in the second FM model

This paper investigates the problem of robust H∞ control for two-dimensional (2D) discrete state delay systems described by the Fornasini-Marchesini (FM) second model. The parameter uncertainties are supposed to be norm-bounded. Our attention is focused on designing H∞ state feedback controllers guaranteeing the asymptotic stability and H∞ performance of the corresponding closed-loop system. A sufficient condition for H∞ disturbance attenuation performance for the nominal 2D discrete state delay system is first obtained. Next, a stabilising state feedback controller is designed such that the resulting closed-loop system is asymptotically stable and achieves a prescribed H∞ disturbance attenuation level. Furthermore, the resulting criteria are extended to robust H∞ control of the uncertain 2D state-delay system. Two examples are given to demonstrate the advantages of the proposed methods.