Summary
The extensions of the Barbashin-Krasovskij theorem to the partial asymptotic stability of the zero solution of a differential system require the boundedness of the uncontrolled coordinates along the solutions. In this paper the Barbashin-Krasovskij method is generalized without supposing «a priori» knowledges on the solutions. At the same time, the results extend one of C. Risito's theorem to nonautonomous differential equations. As an application, stability properties of the equilibrium state of nonholonomic dissipative mechanical systems are studied.
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Hatvani, L. On partial asymptotic stability by the method of limiting equation. Annali di Matematica Pura ed applicata 139, 65–82 (1985). https://doi.org/10.1007/BF01766850
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DOI: https://doi.org/10.1007/BF01766850