Stable fuzzy control system design with pole-placement constraint: an LMI approach

In this paper, the synthesis of an Linear Matrix Inequality (LMI)-based stable fuzzy control system with pole-placement constraint is presented. The requirements of stability and pole-placement region are formulated based on the Lyapunov direct method. By recasting these constraints into LMIs, we formulate an LMI feasibility problem for the design of the fuzzy state feedback control system that guarantees stability and satisfies desired transient responses. This theoretical approach is applied to a nonlinear magnetic bearing system concerning the issue of rotor position control. Simulation results show that the proposed LMI-based design methodology yields better performance than those of a linear local controller or single objective controller. In addition, it is observed that the proposed fuzzy state feedback controller provides superior stability robustness against parameter variations. # 2003 Elsevier Science B.V. All rights reserved.