二次式时滞差分系统稳定区域的估计

Estimates of Stability Region for Quadratic Delay Difference Systems

曾建立了二次式时滞差分系统定量的稳定性结果，其中时滞ｒ＞０是任意的整数；也曾对形式较为简单的二次式时滞差分系统作出了时滞ｒ＜ｒ＊时的稳定区域和渐近稳定区域估计，其中ｒ＊是在一定条件下的最大可接受的时滞．本文将对一般形式的二次式时滞差分系统作出时滞ｒ＜ｒ＊时的稳定区域和渐近稳定区域估计，从而推广已有的相应结果．

The authors have established a quantitative stability result of quadratic delay difference systems, in which the delay r >0 is an arbitrary integer, also, for quadratic delay difference systems of simple form they have given the estimates of stability region and asymptotic stability region with the delay r<r * , where r * is the maximum admissible value of delay under certain conditions.In this paper, for quadratic delay difference systems of general form the estimates of stability region and asymptotic stability region with the delay r<r * were derived so that the known relevant results were generalized.