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Essentially Negative News About Positive Systems

Zappavigna, A. and Colaneri, P. and Kirkland, S. and Shorten, R. (2012) Essentially Negative News About Positive Systems. Working Paper. Elsevier. (Unpublished)

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Abstract

In this paper the discretisation of switched and non-switched linear positive systems using Padé approximations is considered. Padé approximations to the matrix exponential are sometimes used by control engineers for discretising continuous time systems and for control system design. We observe that this method of approximation is not suited for the discretisation of positive dynamic systems, for two key reasons. First, certain types of Lyapunov stability are not, in general, preserved. Secondly, and more seriously, positivity need not be preserved, even when stability is. Finally we present an alternative approximation to the matrix exponential which preserves positivity, and linear and quadratic stability.

Item Type: Monograph (Working Paper)
Additional Information: Preprint submitted to Elsevier
Keywords: Switching positive systems; discretisation; Padé approximation;
Subjects: Science & Engineering > Hamilton Institute
Item ID: 3761
Depositing User: Professor Steve Kirkland
Date Deposited: 19 Jun 2012 15:33
Publisher: Elsevier
Refereed: No
URI:

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