This paper is concerned with the problem of \(H_{\infty }\) control for a class of uncertain switched singular systems with time-varying state delays under asynchronous switching. The asynchronous phenomenon is caused by the choice of controller lagging behind the corresponding subsystem in practice. First, sufficient conditions by finding a novel piecewise Lyapunov–Krasovskii function combining with average dwell time technique are given to guarantee the exponential admissibility of the system. The algebraic equations and differential equations of the original system are proved to be exponentially stable. Then, a condition guaranteeing the \(H_{\infty }\) performance of the original system is derived based on the above analysis. Furthermore, strict LMI formulas for solving the state feedback controller are given. Finally, the effectiveness of the proposed methods is illustrated by numerical examples.

本文关注的是一类不确定开关奇异系统在异步切换下具有时变状态时滞的\（H _ {\ infty} \）控制问题。实际上，异步现象是由于控制器的选择落后于相应子系统而引起的。首先，通过找到新颖的分段Lyapunov–Krasovskii函数并结合平均停留时间技术，给出了充分条件，以保证系统的指数允许性。原始系统的代数方程和微分方程被证明是指数稳定的。然后，保证\（H _ {\ infty} \）的条件基于以上分析得出原始系统的性能。此外，给出了用于求解状态反馈控制器的严格LMI公式。最后，通过数值算例说明了所提方法的有效性。