Stability analysis of sampled-data control systems with multiple time-varying delays

Abstract

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.