关于区间矩阵的稳定度

给区间矩阵 NP,Q]和区间动力系统分别引进了稳定度及鲁棒稳定度的概念 ,并运用矩阵技术及新提出的引理 (判别准则 ) ,仅用界阵 P与 Q的元素 ,获得若干较简捷及实用的稳定度判据 ,从而使区间动力系统 X· ( t) =NP,Q]X( t)的鲁棒稳定度 (含渐近稳定度 )问题得以解决。所得结果包含了黄廷祝教授定常线性系统的结果作为特例 ;并将廖晓昕教授、高为炳院士、李磊博士等人的点阵结果推广到了区间阵 ;将 XUDao- yi教授、施志诚、高为炳等人的稳定性扩展成为稳定度

Degree of Stability for the Interval Matrix

The degree of stability for the interval matrix N and the degree of robust stability for the interval dynamical system are introduced respectively,and new lemma(sufficient condition) is presented as well.Some simple practical criteria of stability are obtained by means of the lemma and matrix technique,which use only the entries of the matrix P and Q.Such that the degree of robust stability (include the degree of asymptotic stability) for the interval dynamical systems X·(t)=NX(t) is considered.The new results obtained in this paper include the results about the degree of stability for the linear systems with constant coefficients presented by HUANG Ting zhu.Also,the results of point matrix in the literature(LIAO Xuao xin 1982,GAO Wei bing 1965,Li Lei 1994)are extended to the interval matrix,and the stability of the interval matrix in earlier papers presented by XU Dao yi and SHI Zhi cheng et al.is generalized into the degree of stability.