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Computing the stability region in delay-space of a tds using polynomial eigenproblems
KTH, School of Computer Science and Communication (CSC).ORCID iD: 0000-0001-9443-8772
2006 (English)In: Proceedings of the 6th IFAC Workshop on Time-Delay Systems, 2006Conference paper (Refereed)
Abstract [en]

 In this work we analyze stability properties of retarded linear time invariant multi-dimensional, multi-delay, time delay systems with respect to perturbations in the delay parameters. We analyze two methods which allow the computation of the critical delays, i.e., the points in delay-space which causes the system to have a purely imaginary eigenvalue. The critical delays are potential stability boundaries as the boundaries of the stability region is necessarily a subset of the critical delays.The two methods originates from a Lyapunov-type condition, which is completely self-contained in this work. The first method corresponds to the case of commensurate delays, for which the the Lyapunov-type condition reduces to a polynomial eigenvalue problem for which the first companion form is exactly the eigenvalue problem occurring in Chen et al. (1995). The second method is the result of a simple substitution which allows the computation of the critical delays of an incommensurate system by solving a quadratic eigenvalue problem. For the scalar multi-delay case we find a closed expression for the critical curves using this method. We confirm the methods by comparing it to previous work and published examples.

Place, publisher, year, edition, pages
Keyword [en]
Time-delay systems, critical delays, quadratic eigenproblems, Kronecker products, stability, stability chart
National Category
Computer and Information Science
URN: urn:nbn:se:kth:diva-53369OAI: diva2:469998
6th IFAC Workshop on Time-Delay Systems, L’Aquila, Italy, 10-12 July 2006
QC 20120206Available from: 2011-12-27 Created: 2011-12-27 Last updated: 2012-02-06Bibliographically approved

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Jarlebring, Elias
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