Digital Library

of the European Council for Modelling and Simulation



A Simple DDS Algorithm For TDS: An Example


Libor Pekar

Published in:



(2015).ECMS 2015 Proceedings edited by: Valeri M. Mladenov, Grisha Spasov, Petia Georgieva, Galidiya Petrova, European Council for Modeling and Simulation. doi:10.7148/2015



ISBN: 978-0-9932440-0-1


29th European Conference on Modelling and Simulation,

Albena (Varna), Bulgaria, May 26th – 29th, 2015


Citation format:

Libor Pekar (2015). A Simple DDS Algorithm For TDS: An Example, ECMS 2015 Proceedings edited by: Valeri M. Mladenov, Petia Georgieva, Grisha Spasov, Galidiya Petrova  European Council for Modeling and Simulation. doi:10.7148/2015-0246



This paper is aimed at the presentation and simulation verification of a novel simple and fast delay dependent stability (DDS) testing algorithm for linear timeinvariant time delay systems (LTI TDS). The algorithm can be used for systems with multiple delays and/or those with many controller parameters. Value ranges of delays and tunable parameters decide about the (exponential) stability of LTI TDS and the goal is to determine such ranges that might not be convex. Our numerical gridding iterative DDS algorithm is based on the finite dimensional approximation of the characteristic quasipolynomial by means of the Taylor series expansion or a Padé-like approach followed by the Regula-Falsi result enhancement. Stability regions are sought through the determination of crossing delays (or parameters) which cause the system stability switching. Numerical simulation experiments performed in MATLAB® environment prove a sufficient accuracy and the practical usability of the proposed DDS algorithm.


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