Title: Fuzzy H_∞ filtering for nonlinear 2D systems in the Roesser 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 study focuses on the H_∞ filtering problem for two-dimensional (2D) discrete Takagi-Sugeno (T-S) fuzzy systems in the Roesser model. The objective is to design a stable filter guaranteeing the asymptotic stability and a prescribed H_∞ performance of the filtering error system. By using a new structure of the fuzzy Lyapunov function, and some analysis techniques, the stability and a prescribed H_∞ performance index are guaranteed for the overall filtering-error system, such that the coupling between the Lyapunov matrix and the system matrices is removed. In addition, sufficient conditions for the existence of such a filter are established in term of linear matrix inequalities (LMIs). When these LMIs are feasible, the explicit expression of the desired filter can be characterised. An illustrative example is presented to demonstrate the effectiveness of the developed results.

Keywords: H_∞ filtering; 2D; two-dimensional fuzzy systems; T-S; Takagi-Sugeno model; linear matrix inequalities; fuzzy Lyapunov function; filter design.

DOI: 10.1504/IJMIC.2019.104376

International Journal of Modelling, Identification and Control, 2019 Vol.33 No.2, pp.169 - 178

Received: 18 Jul 2019
Accepted: 14 Sep 2019
Published online: 06 Jan 2020 *

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