LMI Relaxations for $$mathcal{H }_{infty }$$ and $$mathcal{H }_{2}$$ Static Output Feedback of Takagi–Sugeno Continuous-Time Fuzzy Systems

[摘要] This paper presents new results concerning the problem of static output feedback (mathcal{H }_{infty }) and (mathcal{H }_{2}) control design for continuous-time Takagi–Sugeno (T–S) fuzzy systems. A fuzzy line integral Lyapunov function with arbitrary polynomial dependence on the premise variables is used to certify closed-loop stability with a bound to the (mathcal{H }_{infty }) and (mathcal{H }_{2}) norms, allowing the membership functions 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 fuzzy state feedback control gain is determined by means of linear matrix inequalities (LMIs). Then, the state feedback gain matrices are used in the LMI conditions of the second step that, if satisfied, provide the fuzzy static output feedback control law. The proposed approach also allows the output feedback gains to have independent and arbitrary polynomial dependence on some specific premise variables, selected by the designer, with great advantages for practical applications. The efficiency of the proposed strategy is demonstrated by means of numerical examples and time domain simulations...

[学科分类] 自动化工程

[关键词] Takagi–Sugeno fuzzy systems ;(mathcal{H }_{infty });(mathcal{H }_{2});Static output feedback ;Linear matrix inequalities