On stability tests for continuous and discrete-time linear systems

J.H.F. Ritzerfeld

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

Samenvatting

In order to ensure the stabiltity of an n-th order linear system there are tests (due to Hurwitz and Schur) to check whether the roots of the denominator polynomials of the transfer functions in the continuous and the discretetime case are in the left complex half-plane or within the unit circle, respectively. In this contribution, the parallel treatment developed for both cases leads to a simple and insightful proof for the classical stability tests. Instead of looking at the location of the roots of a polynomial as a purely mathematical problem, a systems approach is used that determines whether the covariance matrices of the associated linear systems in state space are positive definite. The result is that the three critical constraints for stability (given by Jury [3]) are simply found from the determinants of the generating matrices for the covariance. These critical conditions, which are a subset of the n+1 stability constraints, are sufficient if one starts with a stable system and all parameters are varied, for example in an adaptive environment.
Originele taal-2Engels
TitelProceedings of the 16th ProRISC, Annual Workshop on Circuits, Systems and Signal Processing (ProRISC 2005) 17 - 18 November 2006, Veldhoven, the Netherlands
Plaats van productieUtrecht, the Netherlands
UitgeverijTechnology Foundation
Pagina's668-673
ISBN van geprinte versie90-73461-50-2
StatusGepubliceerd - 2005
Evenement2005 Annual Workshop on Circuits, Systems and Signal Processing (ProRISC 2005) - Veldhoven, Nederland
Duur: 17 nov 200518 nov 2005
Congresnummer: 16

Congres

Congres2005 Annual Workshop on Circuits, Systems and Signal Processing (ProRISC 2005)
Verkorte titelProRISC 2005
LandNederland
StadVeldhoven
Periode17/11/0518/11/05
AnderProRISC 2005, Veldhoven, the Netherlands

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  • Citeer dit

    Ritzerfeld, J. H. F. (2005). On stability tests for continuous and discrete-time linear systems. In Proceedings of the 16th ProRISC, Annual Workshop on Circuits, Systems and Signal Processing (ProRISC 2005) 17 - 18 November 2006, Veldhoven, the Netherlands (blz. 668-673). Utrecht, the Netherlands: Technology Foundation.