Title: An LMI approach to design robust H controller for 2-D systems with delays

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 focuses on H controller design for two-dimensional (2-D) discrete state delay systems described by the second Fornasini-Marchesini local state space (FM LSS) model with polytopic uncertainties. The objective is to design a robust state feedback controller such that the corresponding closed-loop system achieves robust asymptotic stability and guarantees a prescribed H performance index for all admissible uncertainties. Based on parameter-dependent Lyapunov functions and Finsler's lemma, a new sufficient condition for H performance analysis of 2-D discrete systems with delays is developed. Then a stabilising state feedback controller is designed. A simulation example is exploited to show the effectiveness of the proposed approach.

Keywords: 2-D state-delayed systems; State feedback; H performance; polytopic uncertainties.

DOI: 10.1504/IJSSE.2019.100335

International Journal of System of Systems Engineering, 2019 Vol.9 No.2, pp.99 - 116

Received: 11 Jul 2018
Accepted: 11 Oct 2018

Published online: 25 Jun 2019 *

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