𝔖 Bobbio Scriptorium
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Ring models for delay-differential systems

✍ Scribed by A.S. Morse

Publisher
Elsevier Science
Year
1976
Tongue
English
Weight
327 KB
Volume
12
Category
Article
ISSN
0005-1098

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✦ Synopsis

SummmT--This paper studies the algebraic structure of linear systems defined over R[A ], the ring of polynomials in X with real coΒ’~cients. Natural definitions of controllability and observab/lity are introduced and properties of R[A]transfer matrix real/zafions are discussed. It is shown that (A .... D. x, ) is a controllable R[A ]-matrix pair if and only if for each set of polynomials A8,,~2 ..... /3,. in R[A] there exists an R[A] feedback matrix F such that det [sl-A -BF] = ~I (s + ~,). By regarding A 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.

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