On qualitative properties of single-delay linear retarded differential equations: Characteristic roots of maximal multiplicity are necessarily dominant. Issue 2 (2020)

• Record Type: Journal Article
• Authors: Mazanti, Guilherme; Boussaada, Islam; Niculescu, Silviu-Iulian
• Is Part Of: IFAC-PapersOnLine. Volume 53:Issue 2(2020)
• Page Start: 4345
• Page End: 4350
• Publication Date: 2020
• Subjects: Time-delay equations -- stability analysis -- spectral methods -- root assignment; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2020.12.2705
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: This paper presents necessary and sufficient conditions for the existence of a real root of maximal multiplicity in the spectrum of a linear time-invariant single-delay equation of retarded type. We also prove that this root is always strictly dominant, and hence determines the asymptotic behavior of the system. These results are based on improved a priori bounds on the imaginary part of roots on the complex right half-plane.