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基于Backstepping反推式设计方法和Lyapunov-Krasovskii泛函,讨论了一类具有三角形结构的非线性时滞系统的鲁棒镇定问题。从系统的最低阶次开始设计,逐步构造Lyapunov-Krasovskii泛函,直到最后得到使得闭环系统渐近稳定的状态反馈控制律。在每一步设计过程中,引入虚拟控制输入与误差变量,重构Lyapunov-Krasovskii泛函简化了设计步骤,放宽假设条件,扩大系统控制律的适用范围。仿真实例表明了结论的有效性。
Based on backstepping design method and Lyapunov-Krasovskii functional, the robust stabilization of a class of nonlinear time-delay systems with triangular structure is discussed. Starting from the lowest order of the system, the Lyapunov-Krasovskii functional is constructed step by step until a closed-loop system asymptotically stable state feedback control law is obtained. In each step of the design process, the virtual control inputs and error variables are introduced. The reconstruction of Lyapunov-Krasovskii functional simplifies the design steps, relaxes the assumptions and expands the applicable scope of the system control law. The simulation example shows the validity of the conclusion.