Stabilization of a class of Takagi-Sugeno fuzzy control systems via piecewise fuzzy Lyapunov function approach

In this paper, the stabilization of Takagi-Sugeno (T-S) fuzzy control systems whose premise variables employ two-overlapped fuzzy partition is investigated. Based on the piecewise fuzzy Lyapunov function and the nonparallel-distributed-compensation (non-PDC) control laws, sufficient conditions for stabilization of T-S fuzzy systems with parametric uncertainties are derived in the form of linear matrix inequalities (LMIs). The piecewise fuzzy Lyapunov function approach avoid the disadvantages of the fuzzy Lyapunov function approach who is valid only when the time derivatives of the membership functions exist in the whole fuzzy region. Moreover, compared to the PDC fuzzy controller, the non-PDC control laws shows greater potential to relax the stability conditions. An illustrative example is given to validate the effectiveness of the proposed approach.