Open AccessInternally positive representations and stability analysis of linear differential systems with multiple time‐varying delays
Author(s) -
De Iuliis Vittorio,
D'Innocenzo Alessandro,
Germani Alfredo,
Manes Costanzo
Publication year - 2019
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2018.5280
Subject(s) - control theory (sociology) , stability (learning theory) , representation (politics) , sign (mathematics) , mathematics , constant (computer programming) , linear system , differential (mechanical device) , simple (philosophy) , delay differential equation , computer science , differential equation , control (management) , mathematical analysis , engineering , machine learning , artificial intelligence , aerospace engineering , philosophy , epistemology , politics , political science , law , programming language
This work introduces the internally positive representation of linear time‐varying delay differential systems, in the general case of multiple time‐varying delays. The technique, previously established for the delay‐free case and recently extended to various classes of linear delay systems, aims at building a positive representation of systems whose dynamics is, in general, not definite in sign, in order to export results that only hold for positive systems to arbitrary ones. In the special case of constant matrices, this leads to a simple and easy to check condition for the delay‐independent stability of differential systems with multiple time‐varying delays. The condition is shown to be less conservative than some well‐known conditions available in the literature. Numerical examples are proposed to validate the theoretical results.