An LMI-Based Controller Design of Uncertain Nonlinear Systems using Takagi-Sugeno Fuzzy Region Model

Robust control of a class of uncertain Takagi-Sugeno (T-S) fuzzy system is investigated in the paper by using fuzzy region concept. The general uncertain T-S fuzzy model with Standard Fuzzy Partition (SFP) inputs is converted into fuzzy region ones. A Fuzzy Region Controller (FRC) is designed based on the fuzzy region concept, and sub-models in a fuzzy region share the same FRC. The relaxed stability conditions for closed-loop fuzzy region systems are derived by using Piecewise Smooth Quadratic (PSQ) Lyapunov function in terms of Linear Matrix Inequalities (LMIs). The derived stability condition, which only requires finding a local common positive definite symmetric matrix P in each operating region, can reduce the conservatism and difficulty in existing stability conditions. Finally, the feasibility and validity of this approach are demonstrated by a numerical example.