Robust H∞ nonlinear control via fuzzy static output feedback

An optimization technique is proposed to represent a class of nonlinear systems by a Takagi-Sugeno uncertain fuzzy model. Then, a robust H_∞ quadratic stabilization problem to the uncertain fuzzy systems via static output feedback is investigated. It is proved that the existence of a set of solvable bilinear matrix inequalities (BMIs) suffices to guarantee the quadratic stabilization of an uncertain fuzzy system in an H_∞ sense. A linear matrix inequality formulation is suggested to alleviate the difficulties of BMI that are inherited from the stabilizability problems via static output feedback control. Both continuous- and discrete-time systems are treated in a unified approach and connections to state feedback and dynamic-output feedback are addressed.