Equivalence of internal and external stability for a class of distributed systems
Equivalence of internal and external stability for a class of distributed systems
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一类分布式系统的内部稳定性和外部稳定性的等价
DOI：
10.1007/bf02570569
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发表时间：
1991
期刊：
影响因子：
--
通讯作者：
Y. Yamamoto
中科院分区：
文献类型：
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作者：
Y. Yamamoto
众所周知，对于无穷维系统，指数稳定性不一定由谱的位置决定。类似地，H ∞空间中的传递函数不需要具有指数稳定的实现。本文针对一类称为伪随机的脉冲响应来解决这个问题。在这个类中，它表明，困难是与经典的复分析，特别是整个函数的指数型。这种整函数的无穷积表示使得证明稳定性确实由谱的位置或由修改的H ∞条件决定成为可能。最后给出了实例来说明理论。
It is well known that for infinite-dimensional systems, exponential stability is not necessarily determined by the location of spectrum. Similarly, transfer functions in theH∞ space need not possess an exponentially stable realization. This paper addresses this problem for a class of impulse responses calledpseudorational. In this class, it is shown that the difficulty is related to classical complex analysis, especially that of entire functions of exponential type. The infinite-product representation for such entire functions makes it possible to prove that stability is indeed determined by the location of spectrum or by a modifiedH∞ condition. Examples are given to illustrate the theory.