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具有零动态仿射非线性系统控制Lyapunov函数的构造
引用本文:蔡秀珊,汪晓东,吕干云.具有零动态仿射非线性系统控制Lyapunov函数的构造[J].控制理论与应用,2007,24(3):391-395.
作者姓名:蔡秀珊  汪晓东  吕干云
作者单位:浙江师范大学,数理与信息工程学院,浙江,金华,321004
基金项目:浙江省自然科学基金资助项目(Y105141); 浙江省教育厅科研基金资助项目(20050291); 浙江师范大学国家基金预研资助项目(2005gjjj021)
摘    要:研究具有零动态仿射非线性系统控制Lyapunov函数的构造问题.提出通过求解一个Lyapunov方程获得可线性化部分的二次型控制Lyapunov函数.由可线性部分的控制Lyapunov函数和零动态部分的Lyapunov函数,通过构造一个正定函数,得到了整个系统的控制Lyapunov函数,且设计了可半全局镇定整个闭环系统的控制律.仿真实例说明了所提出方法的有效性.

关 键 词:非线性系统  控制Lyapunov函数  半全局镇定  零动态
文章编号:1000-8152(2007)03-0391-05
收稿时间:8/5/2005 12:00:00 AM
修稿时间:2005-08-052006-02-23

Constructive control Lyapunov functions for affine nonlinear systems with zero dynamics
CAI Xiu-shan,WANG Xiao-dong,LV Gan-yun.Constructive control Lyapunov functions for affine nonlinear systems with zero dynamics[J].Control Theory & Applications,2007,24(3):391-395.
Authors:CAI Xiu-shan  WANG Xiao-dong  LV Gan-yun
Affiliation:College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua Zhejiang 321004, China
Abstract:The construction of control Lyapunov functions for affine nonlinear systems with zero dynamics is considered in this paper.A method is developed to ensure that a control Lyapunov function for the feedback linearizable part can be obtained by solving a Lyapunov equation.Using the control Lyapunov function of the feedback linearizable part and a Lyapunov function of the zero dynamics,a control Lyapunov function for the overall nonlinear system is then established by constructing a definite function.A state feedback is also designed to semiglobally stabilize the closed-loop system.Finally,a simulation example is given to illustrate the effectiveness of the design.
Keywords:nonlinear systems  control Lyapunov functions  semiglobal stabilization  zero dynamics
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