摘要
将原系统分解为快慢两个子系统,并依据假设得到使快系统渐近收敛的状态反馈控制器.然后基于Lyapunov函数和逆推法构造出慢系统的状态反馈控制器,使得闭环系统对于所有有界干扰是内部稳定的,且从外部扰动输入到输出满足任意小的有界L2增益.通过求出第一个子系统的严格耗散不等式,递推得到全系统的严格耗散不等式,因此控制器设计过程避免了求解Hamilton-Jacobi方程,仿真实例说明了该方法的有效性和可行性.
Dividing a nonlinear singularly perturbed system into the fast and slow subsystems and according to the assumption, a state feedback controller with asymptotic convergence is obtained for the fast subsystem. Then, based on Lyapunov function and the backstepping design technique, a state feedback controller for the slow subsystem is also constructed, which enables the closed-loop system to be internally stable for all bounded interference and satisfies the arbitrarily small bounded L2 gain from exogeneous interference input to its output. The strictly dissipative inequality for the whole system can be deduced through recursive method after getting that for the first subsystem. So, the design process of controller can be done without the solution to Hamilton-Jacobi equation. A simulation example shows the feasibility and effectiveness of the approach proposed.
出处
《东北大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2008年第5期621-624,640,共5页
Journal of Northeastern University(Natural Science)
基金
国家自然科学基金资助项目(60274009)
教育部高等学校博士学科点专项科研基金资助项目(20020145007)
关键词
奇异摄动
快慢子系统
逆推法
L2增益
干扰抑制
singularly perturbed
fast-slow subsystem
backstepping
L2 gain
interference suppression
