An LMI-based Stable Fuzzy Control System Design with Pole Placement Constraints

This paper proposes a systematic design methodology for the Takagi-Sugeno(TS) model based fuzzy control system with guaranteed stability and additional constraints on the closed-loop pole location. These combined two objectives are formulated as a system of LMIs(Linear Matrix Inequalities). Since LMIs intrinsically reflect constraints, they tend to offer more flexibility for combining various constraints on the closed-loop system. To demonstrate the usefulness of the proposed design methodology it is applied to the requlation problem of a nonlinear magnetic bearing system. Simulation results show that the proposed LMI-based design methodology yields not only maximized stability boundary but also the desired transient responses.