超越函数零点全分布在左半复平面的判别准则及其应用  

CRITERION FOR ALL ZERO POINT OF TRANSCENDENTAL FUNCTION DISTRIBUTING IN LEFT SEMI-COMPLEX PLANE AND ITS APPLICATION

作　　者：张孟秋[1] 

机构地区：[1]湖南教育学院数学系,长沙410012

出　　处：《湖南教育学院学报》1995年第5期30-35,共6页Journal of Hunan Educational Institute

摘　　要：本文首先获得了超越函数,零点全分布在左半复平面的判别准则,然后将其应用于时滞直接控制系统获得其解绝对稳定的充分条件,特别当n=1时。In this paper, the criterion for all zero point of transcendental function f_n(λ, e^(-λx))det(a_(ij)+b_(ij)e^(-λx)-S_(ij)λ)_(nxn) distributing in the left semi-complexplane is obtained, and, by applying it, the sufficient condition is obtained for the absolute stability of direct control systems with delay—time(dx)/(dt)=Ax(t)+Bx(t-x)+bf(σ), σ=c^Tx(t). When n=1 the necessary and sufficient condition for absolute stability of the system is a_(11)<0; a_(11)+|b_(11)|≤0; c_1b_1≤0.

关 键 词：超越函数 直接控制系统 零点全分布 左半复平面 

分 类 号：O174.5[理学—数学] O231[理学—基础数学]