Necessary and sufficient condition for neutral-type delay systems: Polynomial approximations

2024/06/21 by Gerson Portilla, Portilla, Gerson, Mathieu Bajodek +3
Business, Management and Accounting · Computer Science · #Advanced Queuing Theory Analysis #Coding theory and cryptography #FOS: Electrical engineering #Matrix Theory and Algorithms #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2406.15581

openalex publication_date 2024/06/21 · openalex created_date 2024/06/26 · openalex updated_date 2026/07/28

Abstract

A new necessary and sufficient stability test in a tractable number of operations for linear neutral-type delay systems is introduced. It is developed in the Lyapunov-Krasovskii framework via functionals with prescribed derivatives. The necessary conditions, which stem from substituting any polynomial approximation of the functional argument, reduce to a quadratic form of monomials whose matrix is independent of the coefficients of the approximation under consideration. In the particular case of Chebyshev polynomials, the functional approximation error is quantified, leading to an estimate of the order of approximation such that the positive semi-definiteness of the functional is verified. Some examples illustrate the obtained results.

Related

• Easily Testable Necessary and Sufficient Algebraic Criteria for Delay-independent Stability of a Class of Neutral Differential Systems
• Asymptotic properties of neutral type linear systems
• On the necessity of sufficient LMI conditions for time-delay systems arising from Legendre approximation
• Necessary and sufficient stability condition for time-delay systems arising from Legendre approximation
• New criteria for boundedness and stability of nonlinear neutral delay differential equations by Krasnoselskii's fixed point theorem