This article is cited in 1 paper

Mathematical logic, algebra and number theory

Some classical number sequences in control system design

A. V. Chekhonadskikh

Novosibirsk State Technical University, pr. K. Marx, 20, 630073, Novosibirsk, Russia

Abstract: 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, Euler partitions.

UDC: 511.623.3

MSC: 34E10,49N35

Received February 20, 2017, published July 11, 2017

Language: English

DOI: 10.17377/semi.2017.14.053

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