非线性非定常系统在经常作用干扰下的稳定性定理——李雅普诺夫间接法  

The Theorem of the Stability of Nonlinear Nonautonomous Systems under the Frequently-Acting Perturbation —— Liapunov's Indirect Method

作　　者：张书顺 商大中 

机构地区：[1]哈尔滨船舶工程学院

出　　处：《应用数学和力学》1991年第7期671-678,共8页Applied Mathematics and Mechanics

摘　　要：研究在经常作用干扰下的稳定性是研究李雅普诺夫意义下稳定性的深入和发展,并且更有实际意义,因为干扰往往并不是一次的.关于经常作用干扰下的稳定性,马尔金提出了一个一般定理;但实用它必须找出满足一定条件的李雅普诺夫函数.这对于非线性非定常系统是很困难的.本文根据李雅普诺夫间接法的原理,将之推广应用到判别非线性非定常系统在经常作用干扰下的稳定性,证明了一个重要结论.In this paper the stability of nonlinear nonautonomous systems under the frequently-acting perturbation is studied. This study is a forward development of the study of the stability in the Liapunov sense; furthermore, it is of significance in practice since perturbations are often not single in the time domain. Malkin proved a general theorem about the subject. To apply the theorem, however, the user has to construct a Liapunov function which satisfies specified conditions and it is difficult to find such a function for nonlinear nonautonomous systems. In the light of the principle of Liapunov's indirect method, which is an effective method to decide the stability of nonlinear systems in the Liapunov sense, the authors have achieved several important conclusions expressed in the form of theorems to determine the stability of nonlinear nonautonomous systems under the frequently-acting perturbation.

关 键 词：非定常系统 稳定性 李氏间接法 

分 类 号：TP271.72[自动化与计算机技术—检测技术与自动化装置]