The notion of homogeneity is extended to time-delay nonlinear systems. Applications of Lyapunov--Krasovskii functionals and Lyapunov--Razumikhin functions for stability investigation are analyzed. The notion of local homogeneity is introduced, relations between stability/instability of the locally approximating dynamics and the original time-delay system are established. A link between homogeneity and input-to-state stability is investigated. Examples of application of the proposed theory are given.
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Efimov et al. (2014) studied this question.
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