纯粹数学与应用数学
純粹數學與應用數學
순수수학여응용수학
PURE AND APPLIED MATHEMATICS
2014年
5期
485-490
,共6页
雷国梁%岳田%宋晓秋
雷國樑%嶽田%宋曉鞦
뢰국량%악전%송효추
线性离散时间系统%一致多项式膨胀性%Lyapunov函数
線性離散時間繫統%一緻多項式膨脹性%Lyapunov函數
선성리산시간계통%일치다항식팽창성%Lyapunov함수
linear discrete-time systems%uniform polynomial expansiveness%Lyapunov function
给出了Banach 空间中线性离散时间系统一致多项式膨胀性的概念,并讨论了其离散特征。借助Lyapunov函数给出了线性离散时间系统满足一致多项式膨胀的充要条件。所得结论将一致指数稳定性、指数膨胀性及多项式稳定性中的若干经典结论推广到了一致多项式膨胀性的情形。
給齣瞭Banach 空間中線性離散時間繫統一緻多項式膨脹性的概唸,併討論瞭其離散特徵。藉助Lyapunov函數給齣瞭線性離散時間繫統滿足一緻多項式膨脹的充要條件。所得結論將一緻指數穩定性、指數膨脹性及多項式穩定性中的若榦經典結論推廣到瞭一緻多項式膨脹性的情形。
급출료Banach 공간중선성리산시간계통일치다항식팽창성적개념,병토론료기리산특정。차조Lyapunov함수급출료선성리산시간계통만족일치다항식팽창적충요조건。소득결론장일치지수은정성、지수팽창성급다항식은정성중적약간경전결론추엄도료일치다항식팽창성적정형。
In this paper we study uniform polynomial expansiveness concept for linear discrete-time systems in Banach spaces. Our main objective is to give discrete characterizations for uniform polynomial expansiveness. As for applications we obtain a necessary and sufficient condition in terms of Lyapunov functions. Well-known results for uniform exponential stability, exponential expansiveness and polynomial stability are extended to the case of uniform polynomial expansiveness.