Insight into stability analysis of time-delay systems using Legendre polynomials. Issue 2 (2020)

• Record Type: Journal Article
• Authors: Bajodek, M.; Seuret, A.; Gouaisbaut, F.
• Is Part Of: IFAC-PapersOnLine. Volume 53:Issue 2(2020)
• Page Start: 4816
• Page End: 4821
• Publication Date: 2020
• Subjects: Time-delay -- Numerical analysis -- Eigenvalues -- Lyapunov stability -- LMI; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2020.12.1029
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: In this paper, a numerical analysis to assess stability of time-delay systems is investigated. The proposed approach is based on the design of a finite-dimensional approximation of the infinite-dimensional space of solutions of the system. Indeed, based on the dynamical coefficients on the sequence made of the first Legendre polynomials, the original time-delay system is modelled by a finite-dimensional model interconnected to a modelling error. Putting aside the interconnection, the resulting finite-dimensional system turns out to be a nice approximation of the time-delay system. Using Padé arguments, the eigenvalues of this finite-dimensional system are proven to converge towards a set of characteristic roots of the original time-delay system. Furthermore, considering now the whole interconnected system and having a deeper look at the interconnection, an enriched Lyapunov-Krasovskii functional is proposed to develop a sufficient condition expressed in terms of linear matrix inequalities for the stability of the time-delay system. Both results are illustrated on a toy example.