This paper addresses the admissibility analysis and the polynomial fuzzy controller design for a class of singular polynomial fuzzy systems with time-varying delay. Firstly, according to Lyapunov stability theory, a sufficient condition is obtained by means of sum-of-squares (SOS) to ensure that the closed-loop singular polynomial fuzzy system is admissible. Secondly, by the help of the two equivalent sets, SOS-based admissibility conditions are proposed to avoid solving the equality conditions and the polynomial fuzzy controller is designed. Finally, three examples validate the usefulness and superiority of the proposed design procedure compared with existing results.

一类具有时变时滞的奇异多项式模糊系统的可容许性分析和多项式模糊控制器设计。首先，根据李雅普诺夫稳定性理论，通过平方和（SOS）获得了充分的条件，以确保闭环奇异多项式模糊系统是可容许的。其次，借助两个等价集，提出了基于SOS的可容许性条件，以避免求解等式条件，并设计了多项式模糊控制器。最后，三个例子验证了所提出的设计程序与现有结果相比的有效性和优越性。