Alternating approximately bisimilar symbolic models for nonlinear control systems with unknown time-varying delays

In this paper we study existence of symbolic models for the class of nonlinear control systems with unknown time-varying delays. We first introduce the notion of incrementally input-delay-to-state stability and characterize it by means of Liapunov-Krasovskii functionals. We then derive sufficient conditions that guarantee existence of symbolic models which are approximately equivalent, in the sense of alternating approximate bisimulation, to the original time-delay system.