标题： 线性时空间不变松弛系统 显示英文标题

标题： Linear time-and-space-invariant relaxation systems

摘要： 本文将线性时不变（LTI）系统中的松弛物理属性推广到线性时间和空间不变（LTSI）系统。 结果表明，松弛的定义特征——完全单调性、被动性和基于记忆的存储——可以无缝地扩展到时空域。 证明了LTSI系统为松弛类型当且仅当其相关的时空Hankel算子是循环单调的。 这意味着存在一个由过去输入唯一定义的基本二次存储泛函，与任何状态空间实现无关。 如同LTI情况一样，证明了LTSI松弛系统的特性是状态空间概念中的存储与输入输出概念中的遗忘记忆泛函相一致的那些系统。 显示英文摘要

摘要： This paper generalizes the physical property of relaxation from linear time-invariant (LTI) to linear time-and-space-invariant (LTSI) systems. It is shown that the defining features of relaxation -- complete monotonicity, passivity, and memory-based storage -- carry over seamlessly to the spatio-temporal domain. An LTSI system is shown to be of relaxation type if and only if its associated spatio-temporal Hankel operator is cyclically monotone. This implies the existence of an intrinsic quadratic storage functional defined uniquely by past inputs, independently of any state-space realization. As in the LTI case, LTSI relaxation systems are shown to be those systems for which the state-space concept of storage coincides with the input-output concept of fading memory functional.