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

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.