Palindromic polynomials, time-reversible systems, and conserved quantities
Palindromic polynomials, time-reversible systems, and conserved quantities
The roots of palindromic and antipalindromic polynomials appear in pairs (s,1/s). A polynomial with such roots is antipalindromic if and only if in addition, it has a root at 1 of an odd multiplicity. The result has applications in system theory: 1) any kernel representation of a discrete-time, time-reversible, scalar, autonomous LTI system is either palindromic or antipalindromic. (Similar statement holds for systems with inputs.) 2) LTI systems with palindromic or antipalindromic kernel representations have nontrivial conserved quantities.
125-130
Markovsky, Ivan
7d632d37-2100-41be-a4ff-90b92752212c
Rao, Shodhan
0823e42a-7524-4702-89f3-8347900d6a8d
Markovsky, Ivan
7d632d37-2100-41be-a4ff-90b92752212c
Rao, Shodhan
0823e42a-7524-4702-89f3-8347900d6a8d
Markovsky, Ivan and Rao, Shodhan
(2008)
Palindromic polynomials, time-reversible systems, and conserved quantities.
In Proceedings of the 16th Mediterranean Conference on Control and Automation.
IEEE.
.
(doi:10.1109/MED.2008.4602018).
Record type:
Conference or Workshop Item
(Paper)
Abstract
The roots of palindromic and antipalindromic polynomials appear in pairs (s,1/s). A polynomial with such roots is antipalindromic if and only if in addition, it has a root at 1 of an odd multiplicity. The result has applications in system theory: 1) any kernel representation of a discrete-time, time-reversible, scalar, autonomous LTI system is either palindromic or antipalindromic. (Similar statement holds for systems with inputs.) 2) LTI systems with palindromic or antipalindromic kernel representations have nontrivial conserved quantities.
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More information
Accepted/In Press date: October 2007
e-pub ahead of print date: 19 August 2008
Additional Information:
palindromic polynomials, time-reversible systems, conserved quantities, behaviors
Venue - Dates:
16th Mediterranean Conference on Control and Automation, Congress Centre, Ajaccio, France, 2008-06-25 - 2008-06-27
Organisations:
Southampton Wireless Group
Identifiers
Local EPrints ID: 264650
URI: http://eprints.soton.ac.uk/id/eprint/264650
PURE UUID: b37fc72f-c2de-4a36-b3ae-88118c89be5d
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Date deposited: 05 Oct 2007
Last modified: 17 Mar 2024 04:04
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Author:
Ivan Markovsky
Author:
Shodhan Rao
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