Banach空间中线性离散时间系统的一致多项式膨胀性

On uniform polynomial expansiveness of linear discrete-time systems in Banach spaces

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.

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.