【摘要】 <正> 其中A为n×n阶实的常矩阵,b≠0,c≠0均为n级常矢量,T表转置,特征方程|A-λE|=0的根的实部皆为负。更多还原

【Abstract】 The main results of the paper are the following:1.If Abc^T=bc^TA,then the necessary and sufficient condition for the absolute stability （N.S.A.S.condition for short） of the systems（Ⅰ） is c^Tb≤0.2.Lemma.If c^Tb≠0,μ≠0,then there exists a nonsingular matrix K such that b=-μKK^Tc.Let b=K^-1b,c=K^Tc,A=K^-1AK.3.If c^Tb≠0 and K satisfies the condition of the lemma,and A^T+A is positive definite,then the N.S.A.S.condition of （Ⅰ） is c^Tb<0.4.If c^Tb≠0,c^TAc≤0,K satisfies the condition of the lemma,and there exists β>0 such that φ（β）>0,then the N.S.A.S. condition of （Ⅰ） is c^Tb<0.5.If c^Tb≠0,c^TAc>0,K satisfies the condition of the lemma,and there exists such that φ（β）>0,then the N.S.A.S.condition of （Ⅰ）is c^Tb>0.更多还原