Abstract
The main aim of this technical note is to present a new approach to studying the asymptotic behavior of nonlinear delay differential systems. Firstly, we develop a new nonlinear delay differential inequality which will be more effective and interesting than earlier ones in. Then we establish a new generalized Barbalat's lemma which can extend and improve earlier ones in. Finally, by combining the obtained generalized Barbalat's lemma with the nonlinear delay differential inequality, we obtain the attracting set and invariant set of the nonlinear delay differential systems.
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