Stability Analysis of time-delay Systems via Bessel Inequality A quadratic separation approach
Résumé
In this paper, new sufficient stability conditions for the asymptotic stability of time-delay systems are presented using the Quadratic Separation approach. The time-delay system is modeled as an interconnected closed-loop system involving a linear transformation and delay-dependent functions, representing the uncertainties brought by the delay. Those complex valued functions are then embedded into adequate norm bounded uncertainties which lead to several stability results. The novelty of this approach relies on the introduction of new dedicated functions which are built in accordance to the Bessel inequality. They allow us to model the system as an uncertain feedback system and to control the accuracy of the inequality. Then, a sequence of LMI conditions is proposed, which tends to the analytical bounds for both delay dependent stability and delay range stability, at least on examples.