Geodesic
Some classical number sequences in control system design
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 620-628 Cet article a éte moissonné depuis la source Math-Net.Ru

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Algebraic tools of LTI control systems design need graphical and analytical structures which depend on dimension of their control parameter space. Essential elements for optimal low-order control systems are the least stable system poles, i.e. the rightmost on the complex plane characteristic roots. Their mutual location is described by critical root diagrams; the algebraic design procedure uses the root polynomials, i.e. factors of characteristic polynomials, which involve only the rightmost poles. From a theoretical point of view it is important to know the dependence between control space dimension and numbers of arising object sets and their asymptotics; they are represented by Fibonacci numbers and partial sums of Euler partitions. From a practical design point of view we need complete lists of required diagrams and polynomials; so we specify the recursive procedure to build a root polynomial list for each control parameter dimension.
Keywords: LTI control systems, system pole, relative stability, Hurwitz function, critical root diagram, root polynomial, Fibonacci numbers
Mots-clés : Euler partitions. 
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A. V. Chekhonadskikh. Some classical number sequences in control system design. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 620-628. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a17/

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