𝒟_U-Admissibility with static output feedback for uncertain descriptor T–S systems

Abstract

This paper deals with the problem of ${\mathcal{D}}_U$-admissibility analysis and synthesis for a class of uncertain continuous fuzzy descriptor systems. By adopting the linear matrix inequality approach and introducing some free matrices, sufficient conditions are established to ensure the ${\mathcal{D}}_U$-admissibility of the considered class of nonlinear uncertain descriptor systems. From this formulated criterion, a static output feedback multi-controller is designed to ensure the admissibility of the closed loop fuzzy descriptor systems and to improve the transient performances in a union of sub-regions. The merit and effectiveness of the proposed conditions are illustrated by two numerical examples.

Keywords:

• ${\mathcal{D}}_U$-Admissibility
• T–S descriptor systems
• $\mathcal{E}\mathcal{E}\mathcal{M}\mathcal{I}$ regions
• static-output feedback
• uncertain

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Mohamed Amin Regaieg http://orcid.org/0000-0002-1430-1352

Mourad Kchaou http://orcid.org/0000-0002-6849-1745

Additional information

Notes on contributors

Mohamed Amin Regaieg

Mohamed Amin Regaieg received his engineering degree in electrical engineering from the National School of Engineering, university of Sfax, Tunisia, in 2015. He is currently working towards a Ph.D. degree at both University of Picardie Jules Verne (UPJV), Amiens, France and National School of Engineering of Sfax (ENIS), Sfax, Tunisia. His research interests include switched systems, singular systems, time-varying delay, analysis and design for T-S descriptor systems, pole placement, nonlinear and switched control and their application to practical engineering systems.

Jérôme Bosche

Jérôme Bosche received the Ph.D. degree at the University of Poitiers in 2003. Since 2005, he has been with the MIS laboratory (Modelling Information and Systems) as a researcher, in Amiens, France. He is also an assistant professor of the department of sciences of the University of Picardie Jules Verne (UPJV), in Amiens. His current research interests include robust analysis and output feedback stabilisation applied to vehicles and renewable energy systems.

Mourad Kchaou

Mourad Kchaou received his Ph.D. degree in Automatic Control from the National School of Engineering, University of Sfax, Tunisia, in 2009. Currently, he is an associate professor with the Department of Electrical Engineering, University of Hail, Saudi Arabia. Since 2000, he holds a researcher position at the Laboratory of Sciences and Techniques of Automation Control and Computer Engineering, National Engineering School of Sfax, University of Sfax, Tunisia. His research interests include fuzzy control, time-delay systems, singular systems and robust control.

Ahmed El Hajjaji

Ahmed El Hajjaji received the Ph.D. degree in automatic control and HDR degree from the University of Picardie Jules Verne (UPJV), France in 1993 and 2000, respectively. He is currently a full professor and head of Automatic control and Vehicle Research Group in MIS Lab (Modeling Information Systems Laboratory) of UPJV. He has been the director of the Professional Institute of Electrical Engineering and Industrial Computing from 2006 to 2012. Since 1994, he has published more than 350 Journal and conference papers in the areas of advanced fuzzy control, fault detection and diagnosis and fault tolerant control and their applications to vehicle dynamics, engine control, power systems, renewable energy conversion systems and to industrial processes. His research interests include fuzzy control, vehicle dynamics, fault-tolerant control, neural networks, maglev systems and renewable energy conversion systems.

Mohamed Chaabane

Mohamed Chaabane was born in Sfax, Tunisia, on 26 August 1961. He received the Ph.D. degree in electrical engineering from the University of Nancy, Nancy, France, in 1991. He is currently a Professor with the National School of Engineering, University of Sfax, where he has been a Researcher with the Laboratory of Sciences and Techniques of Automatic Control and Computer Engineering (Lab-STA) since 1997. From 1988 to 1992, he was an Associate Professor with the University of Nancy, where he was a Researcher at Center of Automatic Control of Nancy (CRAN). The main research interests are in the filed of robust and optimal control, fault tolerant control, delay systems, descriptor systems, fuzzy logic systems and applications of these techniques to fed-batch processes, asynchronous machines, agriculture systems and renewable energy. Currently, he is an associate editor of the International Journal on Sciences and Techniques of Automatic Control and Computer Engineering (www.sta-tn.com).