This paper considers the simultaneous stabilization of a set of nonlinear systems, that involve uncertain nonlinearities besides multiple time-varying delays in the states. Under the assumption that the upper bounds of delays are known, a memoryless simultaneously stabilizing state feedback controller is presented by proposing a control Lyapunov-Krasovskii functional (CL-KF) method. As required to establish the CL-KF approach, a systematic procedure is given to construct CL-KFs for the systems under consideration. By the obtained CL-KFs, a common stabilizing state feedback control law is established to drive all the systems to the origin. Examples are finally given to verify the benefit of the proposed design method.

本文考虑了一组非线性系统的同时稳定，除了状态中的多个时变延迟外，还涉及不确定的非线性。在延迟上限已知的假设下，通过提出控制 Lyapunov-Krasovskii 泛函 (CL-KF) 方法，提出了一种无记忆同步稳定状态反馈控制器。根据建立 CL-KF 方法的要求，给出了为所考虑的系统构建 CL-KF 的系统程序。通过获得的CL-KFs，建立了一个共同的稳定状态反馈控制律来驱动所有系统到原点。最后给出了例子来验证所提出的设计方法的好处。