Internally positive representations and stability analysis of linear differential systems with multiple time‐varying delays. Issue 7 (1st April 2019)

• Record Type: Journal Article
• Authors: De Iuliis, Vittorio; D'Innocenzo, Alessandro; Germani, Alfredo; Manes, Costanzo
• Is Part Of: IET control theory & applications. Volume 13:Issue 7(2019)
• Page Start: 920
• Page End: 927
• Publication Date: 2019-04-01
• Subjects: delays -- stability -- linear systems -- delay systems -- matrix algebra -- time‐varying systems -- Lyapunov methods -- delay‐differential systems; systems whose dynamics -- positive systems -- delay‐independent stability -- multiple time‐varying delays -- internally positive representation -- linear differential systems -- linear time‐varying delay differential systems -- delay‐free case -- linear delay systems; Control theory -- Periodicals; Automatic control -- Periodicals; 629.8312
• DOI: 10.1049/iet-cta.2018.5280
• Languages: English
• ISSNs: 1751-8644

Abstract

Abstract : 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.