$H^2 $-Functions and Infinite-Dimensional Realization Theory
$H^2 $-Functions and Infinite-Dimensional Realization Theory
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DOI：
10.1137/0313013
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发表时间：
1975
期刊：
影响因子：
--
通讯作者：
J. Baras;R. Brockett
中科院分区：
文献类型：
--
作者：
J. Baras;R. Brockett
本文研究了无穷维线性系统的有界算子和无界算子的实现问题。除了得到覆盖基本情况的可实现准则外，我们还讨论了同一系统的规范实现之间的关系。我们发现，A有界的三元组$(A，b，c)$可实现的传递函数集与圆盘$|{S<；1}|$上解析平方可积的复函数空间密切相关，而A无界但生成强连续半群的三元组$(A，b，c)$可实现的传递函数集与半平面上的解析函数和平方可积函数密切相关。这种关系使得更深入地研究传递函数和实现传递函数的模型之间的关系成为可能。举例说明了结果及其应用。
In this paper the realization question for infinite-dimensional linear systems is examined for both bounded and unbounded operators. In addition to obtaining realizability criteria covering the basic cases, we discuss the relationship between canonical realizations of the same system. What one finds is that the set of transfer functions which are realizable by triples $(A,b,c)$ with A bounded is related in a close way to the space of complex functions analytic and square integrable on the disk $| {s < 1} |$, and that the set of transfer functions which are realizable by triples $(A,b,c)$ with A unbounded but generating a strongly continuous semigroup is related in a close way to functions analytic and square integrable on a half-plane. This relation makes possible a deeper study between the transfer function and the models which realize it. Some examples illustrate the results and their applications.