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Improved stabilization conditions for Takagi-Sugeno fuzzy systems via fuzzy integral lyapunov functions

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3 Author(s)
Tognetti, E.S. ; Sch. of Electr. & Comput. Eng., Univ. of Campinas - UNICAMP, Campinas, Brazil ; Oliveira, R.C.L.F. ; Peres, P.L.D.

This paper presents new results concerning the design of state feedback controllers for continuous-time Takagi Sugeno (T-S) fuzzy systems. The conditions, based on a line integral fuzzy Lyapunov function, are specially suitable for T-S fuzzy systems where no information about the time-derivatives of the membership functions is available. The controller is designed through linear matrix inequalities in a two step procedure: at the first step, a stabilizing fuzzy controller is obtained for a relaxed frozen (i.e. time-invariant) T-S fuzzy system. This control gain is then used as an input data at the second step, that provides a stabilizing control law guaranteed by the line-integral Lyapunov function. An extension to cope with H guaranteed cost control of T-S fuzzy systems is also provided. Numerical examples illustrate the advantages of the proposed method when compared to other techniques available in the literature.

Published in:

American Control Conference (ACC), 2011

Date of Conference:

June 29 2011-July 1 2011