An LMI-Based Approach to Static Output Feedback Stabilization of T-S Fuzzy Systems

The problem of static output feedback control design for continuous-time TakagiSugeno (T–S) fuzzy systems is addressed in this paper. The membership functions are modeled in a space defined by the Cartesian product of simplexes, called multi-simplex, and are allowed to vary arbitrarily (i.e. no bounds on the time-derivative of the membership functions are assumed). The static output feedback fuzzy controller is obtained through a two-step procedure: first, a stabilizing fuzzy state feedback control gain is determined by means of linear matrix inequalities (LMIs). Then, the state feedback gain matrices are used in LMI conditions that, if satisfied, provide the fuzzy static output feedback control law. A fuzzy line integral Lyapunov function with arbitrary polynomial dependence on the premise variables is used to assess closedloop stability. The main appeal of the approach is that the output feedback gains can have independent and arbitrary polynomial dependence on some specific premise variables, selected by the designer, with great advantages for practical applications. An example illustrates that the proposed strategy can provide less conservative results when compared to other methods from the literature for output feedback stabilization of continuous-time T–S fuzzy systems.