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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.
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on (Volume:50 , Issue: 11 )
Date of Publication: Nov. 2003