非线性齐次时滞系统H_∞控制  

Nonlinear H_∞ Control of Time-delay Systems with Homogeneous Properties

作　　者：方建印[1] 郭晓丽[1] 程桂芳[1] 

机构地区：[1]郑州大学数学系,河南郑州450052

出　　处：《数学的实践与认识》2005年第5期168-175,共8页Mathematics in Practice and Theory

摘　　要：讨论了非线性齐次时滞系统的H∞控制问题.首先给出了非线性仿射齐次时滞系统的Lyapunov泛函V(x)具体形式,选取适当的λ* ,使得当λ>λ*时系统的Hamilton-Jacobi-Isaacs不等式有解,从而解决了系统的L2 增益问题.文章最后构造了具体状态反馈控制律u(x) ,使时滞Lyapunov泛函V(x)沿闭环系统轨线导数小于零,保证了系统的渐进稳定性,因而解决了系统的H∞控制问题.The problem of H ∞ control and related L 2 gain of nonlinear time-delay systems with homogeneous properties are considered. First of all, Lyapunov function of the systems are given. Then there is a λ * selected suitable, such that λ *>λ Hamilton-Jacobi-Issacs ineaualitis hold. Finally the nonlinear H ∞ control law is given and the problem of H ∞ control of nonlinear time-delay with homogeneous properties is solved.

关 键 词：时滞系统 非线性 LYAPUNOV泛函 齐次 Hamilton H∞控制问题 状态反馈控制律 Jacobi 渐进稳定性 L2增益 闭环系统 不等式 

分 类 号：O231[理学—运筹学与控制论]