稳定性理论中方程组的分解问题

本文分两部分,第一部分研究了由常微分方程所描述的大系统的稳定性,我们研究了常系数线性大系统的稳定性、变系数线性大系统的稳定性以及非自治非线性大系统的稳定性;第二部分研究了由差分方程所描述的大系统的稳定性,利用向量李雅普诺夫函数方法与标量李雅普诺夫函数方法,我们研究了具有时变系数的线性差分大系统的稳定性。对于每个系统,我们构造了具体的李雅普诺夫函数,并得到了关联项的界限。

THE DECOMPOSITION PROBLEM OF SYSTEMS IN STABILITY THEORY

This paper consiste of two parts The first part studies the stability of large scale systems described by ordinary differential equations. The stability of linear large scale systems with constant coefficents and with time varying coefficients and the stability of non-autonomous nonlinear large systems have been investigated. The second part studies the stability of large scale systems described by difference equations. Using the methods of vector Lyapunov functions and scalar Lyapunov functions the au thor investigates the stability of the linear scale difference systems with time Varying coefficients. For every subsystem, the author constructs the concrete Lyapunov functions and the boundaries of interconnecting terms are obtained.