Abstract: The robust Lagrange stabilization problem is considered as a class of uncertain nonlinear systems with infinite equilibria set,called pendulum-like systems. Firstly,sufficient conditions of Lagrange stability for nominal unperturbed pendulum-like systems are derived based on the nonlocal reduction method. Then the static state feedback controller design methods are presented for uncetain pendulum-like systems with time-varying norm-bounded parameter uncertainty to obtain robust Lagrange stability. It is shown that the above problem can be reduced to the existence of the solutions to a set of LMIs.

Key words: nonlocal reduction method, pendulum-like systems, robust Lagrange stability, LMI

摘要： 针对一类特殊的具有多平衡点的非线性系统——类摆系统，研究了其鲁棒Lagrange镇定问题，给出了鲁棒状态反馈控制器的设计方法。在具体的推导过程中，首先基于非局部降阶法，推导了高阶标称类摆系统Lagrange稳定的充分性条件，然后基于此条件，针对具有范数有界参数不确定性的受控高阶类摆系统，给出了使其鲁棒Lagrange稳定的状态反馈控制器设计的充分性条件。所有的可解条件均可化为标准的LMI求解。

关键词: 非局部降阶法, 类摆系统, 鲁棒Lagrange稳定, LMI