On the stability analysis of multiple model systems

Author

Chadli, Mohammed ; Maquin, Didier ; Ragot, Jose

Author_Institution

Centre de Rech. en Autom. de Nancy, Vandoeuvre les Nancy, France

fYear

2001

fDate

4-7 Sept. 2001

Firstpage

1894

Lastpage

1899

Abstract

This paper studies the global asymptotic stability of the nonlinear systems described by the multiple model approach using the Takagi-Sugeno (T-S) fuzzy modelling. New sufficient conditions for the stability of such systems are given. Stability analysis is derived via Lyapunov technique and LMIs (Linear Matrix Inequalities) formulation obtained from BMIs (Bilinear Matrix Inequalities) linearisation. Following a similar approach, sufficient conditions to guarantee the stability of T-S fuzzy systems for both T-S fuzzy controllers and T-S fuzzy observers are derived. The stabilisation of the closed loop continuous T-S fuzzy models is discussed using the well-known PDC (Parallel Distributed Compensation) technique.

Keywords

Lyapunov methods; asymptotic stability; closed loop systems; compensation; fuzzy control; fuzzy systems; linear matrix inequalities; linearisation techniques; nonlinear control systems; observers; BMI linearisation; LMI formulation; Lyapunov technique; PDC technique; T-S fuzzy controller; T-S fuzzy observer; Takagi-Sugeno fuzzy modelling; bilinear matrix inequality linearisation; closed loop continuous T-S fuzzy model; global asymptotic stability; linear matrix inequality formulation; multiple model approach; multiple model system; nonlinear systems; parallel distributed compensation technique; Asymptotic stability; Fuzzy systems; Numerical stability; Observers; Stability analysis; Sufficient conditions; Vectors; Multiple model approach; controllers; nonlinear systems; observers; stability;

fLanguage

English

Publisher

ieee

Conference_Titel

Control Conference (ECC), 2001 European

Conference_Location

Porto

Print_ISBN

978-3-9524173-6-2

Type

conf

Filename

7076198