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On the Essential Instabilities Caused by Fractional-Order Transfer Functions
Joint Authors
Karimi-Ghartemani, Masoud
Merrikh-Bayat, Farshad
Source
Mathematical Problems in Engineering
Issue
Vol. 2008, Issue 2008 (31 Dec. 2008), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2008-11-10
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
The exact stability condition for certain class of fractional-order (multivalued) transfer functions is presented.
Unlike the conventional case that the stability is directly studied by investigating the poles of the transfer function, in the systems under consideration, the branch points must also come into account as another kind of singularities.
It is shown that a multivalued transfer function can behave unstably because of the numerator term while it has no unstable poles.
So, in this case, not only the characteristic equation but the numerator term is of significant importance.
In this manner, a family of unstable fractional-order transfer functions is introduced which exhibit essential instabilities, that is, those which cannot be removed by feedback.
Two illustrative examples are presented; the transfer function of which has no unstable poles but the instability occurred because of the unstable branch points of the numerator term.
The effect of unstable branch points is studied and simulations are presented.
American Psychological Association (APA)
Merrikh-Bayat, Farshad& Karimi-Ghartemani, Masoud. 2008. On the Essential Instabilities Caused by Fractional-Order Transfer Functions. Mathematical Problems in Engineering،Vol. 2008, no. 2008, pp.1-13.
https://search.emarefa.net/detail/BIM-470699
Modern Language Association (MLA)
Merrikh-Bayat, Farshad& Karimi-Ghartemani, Masoud. On the Essential Instabilities Caused by Fractional-Order Transfer Functions. Mathematical Problems in Engineering No. 2008 (2008), pp.1-13.
https://search.emarefa.net/detail/BIM-470699
American Medical Association (AMA)
Merrikh-Bayat, Farshad& Karimi-Ghartemani, Masoud. On the Essential Instabilities Caused by Fractional-Order Transfer Functions. Mathematical Problems in Engineering. 2008. Vol. 2008, no. 2008, pp.1-13.
https://search.emarefa.net/detail/BIM-470699
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-470699