Stability Analysis for Time-Delay Systems using Rekasius´s Substitution and Sum of Squares

In this paper, a new delay-dependent stability analysis for time-delay linear time-invariant (TDLTI) systems is derived. In contrast to many recent approaches, which often utilize Lyapunov-Krasovskii functionals and linear matrix inequalities, an alternative approach is proposed in this paper. The proposed stability analysis is formulated in the frequency domain and investigates the characteristic equation by using the so-called Rekasius substitution and recently established sum of squares techniques from computational semialgebraic geometry. The advantages of the proposed approach are that the stability analysis is often less conservative than many approaches based on Lyapunov-Krasovskii functionals, as demonstrated on a well-known benchmark example, and that the stability analysis is very flexible with respect to additional analysis objectives