From piece-wise constant to continuous time-varying delays: Global Exponential Stability Preservation for Nonlinear Systems Under Sampling

The preservation of the global exponential stability property for the class of fully nonlinear retarded globally Lipschitz systems with time-varying delays under suitable fast sampling is proven through this manuscript. Two main classes of time-varying delays are considered: i) piece-wise constant state delays and ii) continuous-time Lipschitz state delays. Halanay's inequality along with the equivalence between the piece-wise constant delay global exponential stability and measurable delay global exponential stability properties are exploited to demonstrate these results.