| Banach空间中线性离散时间系统的一致多项式膨胀性 |
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| 引用本文： | 雷国梁,岳田,宋晓秋.Banach空间中线性离散时间系统的一致多项式膨胀性[J].纯粹数学与应用数学,2014(5):485-490. |
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| 作者姓名： | 雷国梁 岳田 宋晓秋 |
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| 作者单位： | 湖北汽车工业学院理学院;中国矿业大学理学院; |
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| 基金项目： | 国家自然科学基金(51374199);中央高校基本科研业务费专项资金(2012LWB53) |
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| 摘 要： | 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。
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| 关 键 词： | 线性离散时间系统 一致多项式膨胀性 Lyapunov函数 |
On uniform polynomial expansiveness of linear discrete-time systems in Banach spaces |
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| Institution: | Lei Guoliang, Yue Tian, Song Xiaoqiu (1. School of Science, Hubei University of Automotive Technology, Shiyan 442002, China; 2. College of Science, China University of Mining and Technology, Xuzhou 221008, China) |
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| Abstract: | 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. |
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| Keywords: | linear discrete-time systems uniform polynomial expansiveness Lyapunov function |
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