Root locus analysis for randomly sampled systems

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

1 Citation (Scopus)

Abstract

Root locus analysis is a graphical method to determine how the roots of the characteristic equation of a linear time-invariant feedback loop change with the loop gain. In this paper we show that a similar analysis can be carried out for randomly sampled systems, i.e., controlled linear systems sampled at random times spaced by independent and identically distributed time-varying intervals. For such systems, the roots of a characteristic equation determine the behavior of expected values of signals in the loop. The root locus analysis in this context is especially useful for positive systems, for which (almost sure) stability can be concluded if the roots of the characteristic equation have a negative real part, and it is particularly simple when the distribution of the intervals between sampling times is exponential or Erlang.
Original languageEnglish
Title of host publication2014 European Control Conference (ECC) 24-27 June 2014, Strasbourg, France
Place of PublicationPiscataway: IEEE Service Center.
PublisherEUCA
Pages1619-1624
ISBN (Print)978-3-9524269-1-3
DOIs
Publication statusPublished - 2014

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Locus
Roots
Characteristic equation
Almost Sure Stability
Positive Systems
Graphical Methods
Interval
Feedback Loop
Expected Value
Identically distributed
Linear Time
Time-varying
Linear Systems
Invariant

Cite this

Guerreiro Tomé Antunes, D. J., & Heemels, W. P. M. H. (2014). Root locus analysis for randomly sampled systems. In 2014 European Control Conference (ECC) 24-27 June 2014, Strasbourg, France (pp. 1619-1624). Piscataway: IEEE Service Center.: EUCA. https://doi.org/10.1109/ECC.2014.6862601
Guerreiro Tomé Antunes, D.J. ; Heemels, W.P.M.H. / Root locus analysis for randomly sampled systems. 2014 European Control Conference (ECC) 24-27 June 2014, Strasbourg, France. Piscataway: IEEE Service Center. : EUCA, 2014. pp. 1619-1624
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Guerreiro Tomé Antunes, DJ & Heemels, WPMH 2014, Root locus analysis for randomly sampled systems. in 2014 European Control Conference (ECC) 24-27 June 2014, Strasbourg, France. EUCA, Piscataway: IEEE Service Center., pp. 1619-1624. https://doi.org/10.1109/ECC.2014.6862601

Root locus analysis for randomly sampled systems. / Guerreiro Tomé Antunes, D.J.; Heemels, W.P.M.H.

2014 European Control Conference (ECC) 24-27 June 2014, Strasbourg, France. Piscataway: IEEE Service Center. : EUCA, 2014. p. 1619-1624.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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AB - Root locus analysis is a graphical method to determine how the roots of the characteristic equation of a linear time-invariant feedback loop change with the loop gain. In this paper we show that a similar analysis can be carried out for randomly sampled systems, i.e., controlled linear systems sampled at random times spaced by independent and identically distributed time-varying intervals. For such systems, the roots of a characteristic equation determine the behavior of expected values of signals in the loop. The root locus analysis in this context is especially useful for positive systems, for which (almost sure) stability can be concluded if the roots of the characteristic equation have a negative real part, and it is particularly simple when the distribution of the intervals between sampling times is exponential or Erlang.

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Guerreiro Tomé Antunes DJ, Heemels WPMH. Root locus analysis for randomly sampled systems. In 2014 European Control Conference (ECC) 24-27 June 2014, Strasbourg, France. Piscataway: IEEE Service Center.: EUCA. 2014. p. 1619-1624 https://doi.org/10.1109/ECC.2014.6862601