不确定非线性系统的鲁棒稳定性分析  

Robust Stability of Nonlinear Systems with Uncertainties

作　　者：董海荣[1] 耿志勇[2] 黄琳[2] 

机构地区：[1]北京交通大学电子信息工程学院,北京100044 [2]北京大学力学与工程科学系,北京100871

出　　处：《自动化学报》2004年第4期547-553,共7页Acta Automatica Sinica

基　　金：国家自然科学基金(60304013;60374039;60204007);北京交通大学论文基金资助~~

摘　　要：基于泛函分析和算子理论的方法,从输入输出的角度研究了一类不确定反馈非线性系统的鲁棒稳定性问题.利用K类函数分别描述非线性不确定环节和非线性系统的算子增益,对非线性反馈互联不确定系统的鲁棒稳定性问题进行了研究.接着利用小增益条件的形式进行等价变化,就可将反馈不确定非线性系统的稳定性条件转化成系统非线性算子的范数条件.并通过举例证明了该方法的有效性.Based on functional analysis and operator theory, the problem of robust stability analysis of a more widespread class of nonlinear feedback uncertain system is considered from the view of input/output. It is supposed that the nonlinear uncertain part and the gain of nonlinear operator are described by the constraints of the so called class K functional. Some robust stability conditions are presented, and an equivalent condition which can be explained as small gain condition is given. The result is illustrated to be efficient through an example.

关 键 词：非线性系统 算子 鲁棒稳定性 

分 类 号：O231[理学—运筹学与控制论]