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Time-delay systems are an important class of dynamical systems that provide asolid mathematical framework to deal with many application domains of interest.In this paper we focus on nonlinear control systems with unknown andtime-varying delay signals and we propose one approach to the control design ofsuch systems, which is based on the construction of symbolic models. Symbolicmodels are abstract descriptions of dynamical systems where one symbolic stateand one symbolic input correspond to an aggregate of states and an aggregate ofinputs. We first introduce the notion of incremental input-delay-to-statestability and characterize it by means of Lyapunov-Krasovskii functionals. Wethen derive sufficient conditions for the existence of symbolic models that areshown to be alternating approximately bisimilar to the original system. Furtherresults are also derived which prove the computability of the proposed symbolicmodels in a finite number of steps.

Symbolic Models for Nonlinear Time-Varying Time-Delay Systems via Alternating Approximate Bisimulation