Real curve analysis and stability of time-delay systems

International audienceIn this work, we investigate the asymptotic stability of LTI differential commensurate time-delay systems whose dynamics are defined in the frequency domain by quasi-polynomials of the form f (s, τ) = m j=0 p j (s) e −j τ s. We propose a new approach for studying the stability with respect to the delay: we determine the asymptotic behavior of the roots of the quasi-polynomial near to the critical pairs of f (s, τ) by analysing the intersection of an associated algebraic space curve with sufficiently refined 3D real boxes. Compared to the existing methods, our method does not require any Puiseux series computation