Non-quadratic local stabilization for continuous-time Takagi--Sugeno models

Authors:
Thierry Marie Guerra;Miguel Bernal;Kevin Guelton;Salim Labiod
Affiliations:
LAMIH FRE CNRS 3304, University of Valenciennes Hainaut-Cambrésis, France;Sonora Institute of Technology, 5 de febrero 818 Sur, Col. Centro, C.P. 85000 Ciudad Obregón, Mexico;CReSTIC EA 3804, University of Reims Champagne-Ardenne, Moulin de la Housse, BP 1039, 51687 Reims cedex 2, France;University of Jijel, LAMEL, BP 98, Ouled Aissa Jijel 18000, Algeria
Venue:
Fuzzy Sets and Systems
Year:
2012

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Abstract

This paper is concerned with non-quadratic stabilization of continuous-time Takagi-Sugeno (TS) models. The well-known problem of handling time-derivatives of membership functions (MFs) as to obtain conditions in the form of linear matrix inequalities (LMIs) is overcome by reducing global goals to the estimation of a region of attraction. Instead of parallel distributed compensation (PDC), a non-PDC control law is proposed according to the non-quadratic nature of the Lyapunov function. Examples are provided to show the advantages over the quadratic and some non-quadratic approaches.