OBSERVERS FOR CONTINUOUS NON-LINEAR SYSTEMS CONTAINING UNKNOWN PARAMETERS AND DESCRIBED BY TAKAGI–SUGENO FUZZY MODEL

C. Ghorbel, A. Abdelkrim, and M. Benrejeb

Keywords

Takagi–Sugeno (TS) fuzzy model, linear matrix inequalities (LMI), quadratic Lyapunov function, fuzzy observers, unmeasurable premise variables

Abstract

This paper deals with the stabilizability problem of continuous non-linear systems represented by Takagi–Sugeno’s fuzzy model. These systems contain unknown parameters. Based on the quadratic Lyapunov function, new update law and LMI (linear matrix inequality) formulation are developed, respectively, to estimate the unknown parameters vector and to guarantee the stability. The case of an unstable continuous non-linear of third-order system is considered to illustrate the proposed approach.

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