On the stability of delay-differential systems in the behavioral framework

In the behavioral approach, a linear time-invariant (LTI) delay-differential system is naturally introduced by Glusing-Luerssen (1997) as a continuous-time system whose dynamics are governed by a set of delay-differential equations, involving both painted and distributed delay operators. For this class of systems the notion of autonomy is introduced and characterized. Finally, asymptotic stability of autonomous delay-differential systems is investigated.