Output feedback LMI tracking control conditions with H∞ criterion for uncertain and disturbed T-S models

Badr Mansouri, Noureddine Manamanni, Kevin Guelton, Alexandre Kruszewski et Thierry-Marie Guerra

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.

Mots clés

Tracking control; Output feedback; Fuzzy Takagi–Sugeno models; Linear matrix inequality (LMI); Quadratic stability; H∞ criterion