Output feedback LMI tracking control conditions with H∞ criterion for uncertain and disturbed TS models

Abstract : 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∞ 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.
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Badr Mansouri, Noureddine Manamanni, Kevin Guelton, Alexandre Kruszewski, Thierry-Marie Guerra. Output feedback LMI tracking control conditions with H∞ criterion for uncertain and disturbed TS models. Information Sciences, Elsevier, 2009, 179 (4), pp.446-457. ⟨10.1016/j.ins.2008.10.007⟩. ⟨hal-00793235⟩

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