This paper studies the finite-time ${\mathcal {H}}_{\infty }$ 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 ${\mathcal {H}}_{\infty }$ 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 ${\mathcal {H}}_{\infty }$ control approach is finally illustrated via numerical simulations.

中文翻译：

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TS模糊系统的有限时间H∞控制器综合

本文研究了有限时间 ${\mathcal {H}}_{\infty }$ 受外部干扰的 T-S 模糊系统的控制问题。在控制李雅普诺夫函数技术和有限时间李雅普诺夫定理的基础上，开发了一种新的模糊控制方法，使闭环模糊系统具有有限时间稳定和保证 ${\mathcal {H}}_{\infty }$ 表现。结果表明，与通过控制 Lyapunov 函数技术对非线性系统进行有限时间控制的许多现有控制方法相比，所提出的控制方法在设计模糊控制器之前不需要存在 Lyapunov 函数，因此，可以同时设计有限时间控制器和相应的李雅普诺夫函数。根据线性矩阵不等式提供了如何获得模糊控制器的过程。此外，估计状态轨迹到达其期望目标所花费的时间的上限。提出的有限时间的有效性 ${\mathcal {H}}_{\infty }$ 最后通过数值模拟来说明控制方法。