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On stability properties of time-varying systems with delays

We consider several stability properties in the framework of input-to-state stability for time-varying systems with delays. By following a natural approach to convert a time-varying system to an auxiliary time-invariant system, we obtain several results including Razumikhin-type stability criteria, Razumikhin-Lyapunov functions with non-strict decay rates, and cyclic small-gain theorems for time-varying systems with delays.