LMI-based tracking control for Takagi-Sugeno fuzzy model

Mohamed Amine.BEN BRAHIM LA.R.A Laboratory National Engineering School of Tunis Tunis,Tunisia mohamedamine.benbrahim@enit.rnu.tn C.GHORBEL, A.ABDELKRIM and M.BENREJEB LA.R.A Laboratory National Engineering School of Tunis Tunis,Tunisia chekib.ghorbel@yahoo.fr afef.abdelkrim@esti.rnu.tn mohamed.benrejeb@enit.rnu.tn Abstract — This present paper deals with the problem of control for Takagi-Sugeno fuzzy model. Based on the quadratic Lyapunov function, an LMI (Linear Matrix Inequality) formulation is suggested to make possible the convergence of the state vector of the discrete-time system to the origin. A first application addresses the inverted pendulum fourth-order unstable system that is modeled by the fuzzy Takagi-Sugeno approach. A second application is a fourth order unstable nonlinear complex system which is studied to illustrate the efficiency of th e LMI formulation. Keywords-Multimodel,fuzzyTakagi-Sugeno,LMI approach, inverted pendulum I. iI

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