Abstract
In this letter, the notion of GALES (Global Asymptotic Local Exponential Stability) is extended to nonlinear systems described by Retarded Functional Differential Equations. Necessary and sufficient Lyapunov-Krasovskii conditions ensuring the GALES of nonlinear time-delay systems are provided. The conditions related to the lower bound and to the dissipation rate of the Lyapunov-Krasovskii functional involve only the current value of the solution, making the provided tool easy to use. An example validating the results is presented.
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