This paper deals with the stability analysis of sampled-data control systems with a centralized controller and multiple actuators, where different controller-actuator delays exist. Via the input-delay approach, a sampled-data control system with multiple time-varying delays is modeled as a linear time-delay system. Though some existing criteria for time-delay systems can be applied to analyze the stability of the original system, the results are conservative since these criteria do not consider the sampling effects properly. To reduce the conservatism, a new looped-functional, which takes advantage of the hybrid characteristic of the sampled-data control system model, is proposed. Meanwhile, a new Lyapunov-Krasovskii functional that aims at fully benefiting from the Wirtinger-based inequality and utilizing the relationship information among the states associated with different delays is constructed. Based on the proposed functionals, a new stability condition for sampled-data control systems with multiple time-varying delays is presented in the form of linear matrix inequalities. Numerical examples are given to illustrate the advantages and effectiveness of the proposed method.

本文涉及具有集中控制器和多个执行器的采样数据控制系统的稳定性分析，其中存在不同的控制器-执行器延迟。通过输入延迟方法，将具有多个时变延迟的采样数据控制系统建模为线性时滞系统。尽管可以将一些现有的时滞系统标准用于分析原始系统的稳定性，但是由于这些标准未适当考虑采样效果，因此结果是保守的。为了减少保守性，提出了一种新的循环功能，该功能利用了采样数据控制系统模型的混合特性。与此同时，构造了一个新的Lyapunov-Krasovskii函数，该函数旨在充分利用基于Wirtinger的不等式并利用与不同延迟相关的状态之间的关系信息。基于所提出的函数，以线性矩阵不等式的形式给出了具有多个时变时滞的采样数据控制系统的新稳定性条件。数值算例说明了该方法的优点和有效性。