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Computing Critical delays for time delay systems with multiple delays
TU Braunschweig, Germany.ORCID iD: 0000-0001-9443-8772
2006 (English)Conference paper, Presentation (Refereed)
Abstract [en]

In this work we present a method to analyze the robustness of stability of a time-delay system (TDS) with respect to the delays. This is done by computing the delays for which the system has a purely imaginary eigenvalue. These delays, called critical delays , generate potential points for a stability switch, i.e., the point where the system switches from a stable to unstable. To derive the method, we find a Lyapunov-type equation , equivalent to the characteristic equation of the TDS. Unlike the characteristic equation, the Lyapunov-type equation does not have any non-exponential terms if the eigenvalue is imaginary. This allows us to solve the Lyapunov-type equation by rewriting it to a quadratic eigenvalue problem for which there are efficient numerical methods. For the scalar case, we find a new explicit expression for the curves in the stability chart. The method is applied to previously solved examples as well as previously unsolved problems of larger dimension.

Place, publisher, year, edition, pages
Keyword [en]
Multiple time delay, Critical delays, Hopf bifurcation, Robustness, Stability, Lyapunov operators, Polynomial eigenvalue problems
National Category
Computer and Information Science
URN: urn:nbn:se:kth:diva-53368OAI: diva2:469997
Reglermöte, Stockholm, 2006, May 30-31

NV 20150504

Available from: 2011-12-27 Created: 2011-12-27 Last updated: 2015-05-04Bibliographically approved

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Jarlebring, Elias
Computer and Information Science

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