A Gain-Scheduling Control Approach for Takagi-Sugeno Fuzzy Systems Based on Linear Parameter-Varying Control Theory

Due to the universal approximation capability of Takagi-Sugeno (T-S) fuzzy models for nonlinear dynamics, many control issues have been investigated based on fuzzy control theory. In this paper, a transformation procedure is proposed to convert fuzzy models into linear fractional transformation (LFT) models. Then, T-S fuzzy systems can be regarded as a special case of linear parameter-varying (LPV) systems which proved useful for nonlinear control problems. The newly established connection between T-S fuzzy models and LPV models provides a new perspective of the control problems for T-S fuzzy systems and facilitates the fuzzy control designs. Specifically, an output feedback gainscheduling control design approach for T-S fuzzy systems is presented to ensure globally asymptotical stability and optimize H_∞ performance of the closed-loop systems. The control synthesis problem is cast as a convex optimization problem in terms of linear matrix inequalities (LMIs). Two examples have been used to illustrate the efficiency of the proposed method.