基于非局部降阶法的类摆系统鲁棒Lagrange镇定

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.

Robust Lagrange Stabilization of Uncertain Pendulum-Like Systems Based on Nonlocal Reduction Method

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.