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

Authors: Khalid Badie; Mohammed Alfidi; Zakaria Chalh

Addresses: Engineering, Systems and Applications Laboratory, National School of Applied Sciences, BP 72, My Abdallah Avenue Km 5 Imouzzer Road, Fez, Morocco ' Engineering, Systems and Applications Laboratory, National School of Applied Sciences, BP 72, My Abdallah Avenue Km 5 Imouzzer Road, Fez, Morocco ' Engineering, Systems and Applications Laboratory, National School of Applied Sciences, BP 72, My Abdallah Avenue Km 5 Imouzzer Road, Fez, Morocco

Abstract: 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.

Keywords: 2D discrete system; robust H_∞ control; FM second model; linear matrix inequality; LMI.

DOI: 10.1504/IJSCC.2019.100531

International Journal of Systems, Control and Communications, 2019 Vol.10 No.3, pp.218 - 234

Received: 02 Mar 2018
Accepted: 25 Oct 2018
Published online: 29 Jun 2019 *

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