Finite-Time $\mathcal{H}_{\infty}$ Controller Synthesis of T–S Fuzzy Systems
针对受外部扰动的T-S模糊系统，提出一种基于控制Lyapunov函数和有限时间Lyapunov定理的模糊控制方法，可同时设计控制器和Lyapunov函数，保证闭环系统有限时间稳定并满足H∞性能，并用线性矩阵不等式给出求解步骤。
This paper studies the finite-time H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control problem of T-S fuzzy systems subject to external disturbances. A novel fuzzy control approach is developed on the basis of the control Lyapunov function technique and the finite-time Lyapunov theorem so that the closed-loop fuzzy system is finite-time stable with guaranteed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance. It is shown that the proposed control approach does not require the existence of a Lyapunov function before design of the fuzzy controller in comparison with many existing control approaches to finite-time control of nonlinear systems via the technique of control Lyapunov functions, and thus, the finite-time controller and the corresponding Lyapunov function can be designed simultaneously. The procedures on how to obtain the fuzzy controller are provided in terms of linear matrix inequalities. Moreover, an upper bound on the time taken for state trajectories to arrive at their desired targets is estimated. The effectiveness of the proposed finite-time H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control approach is finally illustrated via numerical simulations.