Synthesis of an LMI-based fuzzy control system with guaranteed optimal H∞ performance

This paper proposes a systematic design methodology for the Takagi-Sugeno (TS) model based fuzzy control system with guaranteed H _∞ performance and additional constraints on the closed-loop pole location. These combined two objectives are formulated as a convex optimization problem involving LMIs (linear matrix inequality). To demonstrate the usefulness of the proposed design methodology, it is applied to the robust regulation problem of a nonlinear magnetic bearing system. Simulation results show that the proposed fuzzy controller yields the optimal disturbance rejection performance and the desired transient responses simultaneously