Ring models for delay-differential systems
Ring models for delay-differential systems
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延迟差分系统的环模型
DOI：
10.1016/0005-1098(76)90013-3
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发表时间：
1974
期刊：
影响因子：
--
通讯作者：
A. Morse
中科院分区：
文献类型：
--
作者：
A. Morse
本文研究了定义在R[λ]上的线性系统的代数结构，R是实系数λ中的多项式环。引入了能控性和能观性的自然定义，讨论了R[λ]-转移矩阵实现的性质。证明了(An×n，Dn×m)是可控R[λ]-矩阵对当且仅当对每个多项式集合β1，β2，…，βn，在R[λ]中存在R[λ]反馈矩阵F使得detsi−A−BF]=∏i=1n(S+βi)。通过将λ视为适当定义的延迟算子，解释了如何将这一结果应用于时滞微分系统以控制动态响应。
This paper studies the algebraic structure of linear systems defined over R[λ], the ring of polynomials in λ with real coefficients. Natural definitions of controllability and observability are introduced and properties of R[λ]-transfer matrix realizations are discussed. It is shown that (An×n,Dn×m) is a controllable R[λ]-matrix pair if and only if for each set of polynomialsβ1,β2,…,βn, in R[λ] there exists an R[λ] feedback matrixFsuch that detsI−A−BF]=∏i=1n(s+βi). By regarding λ as a suitably defined delay operator, it is explained how this result might be applied to delay-differential systems in order to control dynamic response.