Stability Study of Mamdani’s Fuzzy Controllers Applied to Linear Plants

Anis SAKLY, Basma ZAHRA, Mohamed BENREJEB
Unité de recherche LARA Automatique
Ecole Nationale d’Ingénieurs de Tunis, BP 37, Belvédère 1002 Tunis, Tunisie

Abstract: A stability study approach of fuzzy control systems, in the continuous case and the discrete one, is presented in this paper. This approach is based on vector norms corresponding to a Lyapunov’s vector function and allowing to establish sufficient conditions for global asymptotic stability of controlled linear systems by Mamdani’s fuzzy controllers. The considered fuzzy regulators are of type PI and have particular fuzzy partition for input variables corresponding to Lur’e type systems.

Keywords: Mamdani’s fuzzy controllers, global asymptotic stability, vector norms, arrow’s form matrix.

Anis Sakly was born in 1970. He received his Electrical Engineering diploma in 1994 from the National Engineering School of Monastir (ENIM), Tunisia. Then, he received the doctorate in Electrical Engineering in 2005 from the National Engineering School of Tunis (ENIT). He is currently teaching in the ENIM. His research interests are in fuzzy control, particularly stability analysis and establishment of fuzzy control systems.

Basma Zahra was born in 1978. She received her Electrical Engineering diploma in 2003 from the National Engineering School of Sfax (ENIS), Tunisia. She is currently preparing her doctorate in Electrical Engineering in the National Engineering school of Tunis (ENIT) about analysis and synthesis of PI fuzzy control systems.

Mohamed Benrejeb was born in 1950. He received the Engineering diploma in 1973 from the North Industrial Institute (IDN currently central school of Lille), France. In 1976 he received the engineering doctor diploma in Automatic from Technology and Science university of Lille and the doctorate es physics sciences from the same university in 1980. He is currently professor in higher education in the National Engineering School of Tunis (ENIT) and the Central School of Lille. His fields of research include system control, modelisation, analysis and synthesis of certain and uncertain continuous systems by conventional or nonconventional approaches and concern recently discrete systems.

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CITE THIS PAPER AS:
Anis SAKLY, Basma ZAHRA, Mohamed BENREJEB, Stability Study of Mamdani’s Fuzzy Controllers Applied to Linear Plants, Studies in Informatics and Control, ISSN 1220-1766, vol. 17 (4), pp. 441-452, 2008.