A simple DDS algorithm for TDS: An example

Abstract

This paper is aimed at the presentation and simulation verification of a novel simple and fast delay dependent stability (DDS) testing algorithm for linear time-invariant 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. © ECMS Valeri M. Mladenov, Petia Georgieva, Grisha Spasov, Galidiya Petrova (Editors).