线性离散时间系统的非一致多项式膨胀性

On Nonuniform Polynomial Expansiveness of Linear Discrete-time Systems

给出了Banach空间中线性离散时间系统一致与非一致多项式膨胀性的概念,使其在相应空间中范数的增长速度不快于指数型增长,并用实例阐释了二者的关系.借助于指数型膨胀性的研究方法,讨论了其非一致多项式膨胀性的离散特征.作为应用,利用Lyapunov函数给出了相应概念的充要条件.得到了指数膨胀性理论中一些经典结论在非一致多项式膨胀情形下的变形.

In this paper we study uniform and nonuniform polynomial expansiveness concepts for linear discrete-time systems which are defined in a Banach space and whose norms can increase not faster than exponentially.Some illustrating examples clarify the relations between these concepts.Based on the extension of techniques for exponential expansiveness to the case of polynomial expansiveness,our main objective is to give discrete characterizations for nonuniform polynomial expansiveness.As for applications we obtain a necessary and sufficient condition in terms of Lyapunov functions.The obtained results are generalizations of well-known theorems about the exponential expansiveness.