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A nonlinear version of Halanay's inequality for the uniform convergence to the origin

  • * Corresponding author: e-mail pierdomenico.pepe@univaq.it

    * Corresponding author: e-mail pierdomenico.pepe@univaq.it

This article was recruited by Fabian Wirth

The work has been supported in part by grant MIUR-FFABR 2017

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  • A nonlinear version of Halanay's inequality is studied in this paper as a sufficient condition for the convergence of functions to the origin, uniformly with respect to bounded sets of initial values. The same result is provided in the case of forcing terms, for the uniform convergence to suitable neighborhoods of the origin. Related Lyapunov methods for the global uniform asymptotic stability and the input-to-state stability of systems described by retarded functional differential equations, with possibly nonconstant time delays, are provided. The relationship with the Razumikhin methodology is shown.

    Mathematics Subject Classification: Primary: 93C23, 93D05, 93D20, 93D25; Secondary: 39B72, 34D23, 34D05, 26A46, 26A48.


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