【摘要】 本文首先研究变系数线性系统{x₁=a₁₁（t）x₁+a₁₂（t）x₂x₂=a₂₁（t）x₁+a₂₂（t）x₂的 V 函数构造,然后用类比法研究非线性非驻定系统{x₁=a₁₁（t）f₁（x₁）+a₁₂（t）f₂（x₂）x₂=a₂₁（t）f₃（x₁）+a₂₂（t）f₄（x₂）的 V 函数构造,并利用本文所建立的 V 函数研究了系统{x₁=a₁₁（t）f₁（x₁）+a₁₂（t）f₂（x₂）+e₁（t）x₂=a₂₁（t）f₃（x₁）+a₂₂（t）f₄（x₂）+e₂（t）的解的一致有界性.更多还原

【Abstract】 It is well known that the key problem of Liapunov’s stability theory is how to construct Liapunov functions.For example,E.A Barbasin gave detailed sumtnarizations for it,but they were mainly concerned with autonomous systems. In this paper,we first study the construction of Liapunov functions for linear systems with time-varying coefficients,and then,by analogy,generalize the construction to a class of nonlinear nonautonomous systems.The constr- uction in this paper is a generalization of the works due to E.A.Barbasin.更多还原