�ber die algebraischen Kriterien f�r die Stabilit�t von Regelungssystemen

Cremer, Helmuth; Effertz, F. H.

doi:10.1007/bf01360969

Cited by 23 publications

(5 citation statements)

References 20 publications

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“…We present here but some important data, more details can be found in [6]. Cauchy (1837) showed that the number of roots of a polynomial in a given region of the complex plane can be expressed by the index of a certain rational function.…”

Section: From the History Of The Problemmentioning

confidence: 99%

On stable polynomials

Nekvinda¹

1989

Appl. Math.

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Section: From the History Of The Problemmentioning

confidence: 99%

On stable polynomials

Nekvinda¹

1989

Appl. Math.

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“…Die Umwandlung eines linearen Gleichungssystems in ein lineares Differentialgleichungssystem wird vorgenommen, weil Stabilitätskriterien für derartige Systeme bereits seit langem bekannt sind und von Mathematikern ausführlich behandelt wurden (siehe dazu [6] und die dort angegebene Literatur). Außerdem glaubte man [5], die Integrationsschaltung liefere genauere Ergebnisse.…”

Section: Allgemeine Betrachtungunclassified

Die Lösung linearer Gleichungssysteme auf dem elektronischen Analog-Rechner/ The solution of a system of linear equations with the electronic analog computer

Irnich¹

1963

it - Information Technology

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Die vorliegende Arbeit befaßt sich mit dem Problem, lineare Gleichungssysteme auf dem elektronischen Analog-Rechner nur mit Hilfe von Summierern zu lösen. Die dabei normalerweise auftretenden Arten der Instabilität werden aufgezeigt und ein Weg angegeben, zu zuverlässigen Lösungen zu gelangen. Die bei dieser Methode zu beachtenden MaximaiKoeffizienten wurden für Gleichungssysteme bis 30. Grades ausgerechnet. Als Beispiel wird ein System vierten Grades behandelt und gelöst.The present paper is concerned with the problem of solving systems of linear equations with the help of the electronic analog computer just using summing amplifiers. The types of instabilities that normally occur with this procedure are discussed and a method in obtaining reliable solutions is given. The maximal coefficients that must occur with this method are solved for systems of linear equations with up to 30 unknowns. As an example a system with four unknowns is discussed and solved.

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“…Using the Orlando's formula (8) corresponding to a monic characteristic polynomial of degree N ≥ 2, we introduce a hypersurface sitting in R N (to be used in Sect. 3) as follows.…”

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confidence: 99%

Identification of generic stable dynamical systems taking a nonlinear differential approach

Salehani¹

2018

Discrete &Amp; Continuous Dynamical Systems - B

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Identifying new stable dynamical systems, such as generic stable mechanical or electrical control systems, requires questing for the desired systems parameters that introduce such systems. In this paper, a systematic approach to construct generic stable dynamical systems is proposed. In fact, our approach is based on a simple identification method in which we intervene directly with the dynamics of our system by considering a continuous 1-parameter family of system parameters, being parametrized by a positive real variable , and then identify the desired parameters that introduce a generic stable dynamical system by analyzing the solutions of a special system of nonlinear functional-differential equations associated with the-varying parameters. We have also investigated the reliability and capability of our proposed approach. To illustrate the utility of our result and as some applications of the nonlinear differential approach proposed in this paper, we conclude with considering a class of coupled spring-mass-dashpot systems, as well as the compartmental systems-the latter of which provide a mathematical model for many complex biological and physical processes having several distinct but interacting phases.

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�ber die algebraischen Kriterien f�r die Stabilit�t von Regelungssystemen

Cited by 23 publications

References 20 publications

On stable polynomials

On stable polynomials

Die Lösung linearer Gleichungssysteme auf dem elektronischen Analog-Rechner/ The solution of a system of linear equations with the electronic analog computer

Identification of generic stable dynamical systems taking a nonlinear differential approach

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