On delay (in)dependent stability for TDS

Abstract

A preliminary-study contribution to delay dependent (DDS) and independent (DIS) stability of control systems with multiple delays is focused in this paper. We first introduce some basic facts about the spectral properties of such systems and a recently developed DIS method is concisely described. Then our simple and applicable numerical gridding iterative DDS algorithm based on the finite dimensional approximation of the characteristic quasipolynomial by means of the Taylor series expansion and the Regula-Falsi method is presented. The methodologies are used and verified by a simulation example of control a delayed feedback system with an unstable plant with two delays. Since it is shown that the system is not DIS, the DDS feature with respect to delay deviations is investigated via the proposed algorithm. Numerical experiments indicate a very good correspondence between the DDS algorithm results and the searching of crossing delays by using the QuasiPolynomial matrix Rootfinder. © 2015 IEEE.