摘要
本文研究了方程d/(dt)[x(t)-Cx(t-r)]=Ax(t)+Bx(t-r)的特征根在复平面上的分布,从而得出了关于稳定性和有界性的条件。
This paper has discussed the distributon of the characteristic roots. of the NFDEs:d/dt[x(t)-Cx(t-r)]=Ax(t)+Bx(t-r) on the complex plane, and bta(?)ned the stability and boundedness conditions. All the Theorem2 to Theorem 6 are about the distribution of the characteristic roots of the NFDEs on complex plane. Theorem 7 is about the exponential—asympotatical stability of the solution of the NFDEs. Theorem 8 is about theniform—ultimate boundedness. In this paper, The method used to analye the roots of the characteristic equations of the NFDEs by the E·Picard's theorem about the order of transcendental entire functions anp the number of the w—qoints (Lemma 1) and a theorem about a convergeou unded reulagr function sequence (Lemma 2) is very new and valid.
