一类广义非线性系统的H_∞控制  

H_∞ Control for a Class of Nonlinear Singular Systems

作　　者：董心壮[1] 张庆灵[1] 

机构地区：[1]东北大学理学院,辽宁沈阳110004

出　　处：《东北大学学报（自然科学版）》2004年第7期625-628,共4页Journal of Northeastern University(Natural Science)

基　　金：教育部骨干教师基金资助项目.

摘　　要：研究一种具有特殊形式的广义非线性系统的状态反馈H∞控制器设计问题·此类系统的状态方程可以分成线性部分和非线性部分·利用广义Lyapunov函数和Lyapunov方程,首先给出广义非线性系统零解渐近稳定的充分条件,然后以代数Riccati不等式的形式,得到广义非线性系统零解渐近稳定且具有H∞范数约束的条件,进而在此基础上给出静态状态反馈H∞控制器存在的充分条件,保证闭环系统具有上述性能,并利用Lyapunov方程的解提出相应控制器的构造方法,最后提供一个数值算例以证明文中结论的有效性·The design of static state feedback H_∞ controllers is discussed for a special class of nonlinear singular systems of which the state equation can be divided into linear part and nonlinear part. By means of the generalized Lyapunov function and Lyapunov equation, a sufficient condition is given such that a nonlinear singular system is zero solution asymptotically stable. Then, a sufficient condition is derived in terms of algebraic Riccati inequality which makes the nonlinear singular system zero solution asymptotically stable with a H_∞ norm constraint. Further, the existence condition of a state feedback H_∞ controller is also given guaranteeing the above performance of the resulting closed-loop system. Moreover, the design method of such a controller is provided in terms of the solution to Lyapunov equation. An example is given to prove the validity of the results.

关 键 词：广义非线性系统 广义Lyapunov函数 零解渐近稳定 H∞范数约束 状态反馈 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]