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Output feedback LMI tracking control conditions with $$H_\infty$$ criterion for uncertain and disturbed T-S models. (English) Zbl 1158.93024
Summary: This work concerns the tracking problem of uncertain Takagi-Sugeno (T-S) continuous fuzzy model with external disturbances. The objective is to get a model reference based output feedback tracking control law. The control scheme is based on a PDC structure, a fuzzy observer and a $$H_{\infty }$$ performance to attenuate the external disturbances. The stability of the whole closed-loop model is investigated using the well-known quadratic Lyapunov function. The key point of the proposed approaches is to achieve conditions under a LMI (linear matrix inequalities) formulation in the case of an uncertain and disturbed T-S fuzzy model. This formulation facilitates obtaining solutions through interior point optimization methods for some nonlinear output tracking control problems. Finally, a simulation is provided on the well-known inverted pendulum testbed to show the efficiency of the proposed approach.

MSC:
 93C42 Fuzzy control/observation systems 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93C15 Control/observation systems governed by ordinary differential equations 93B36 $$H^\infty$$-control
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