Asymptotic behaviors of solutions of a class of time-varying differential equations. (English) Zbl 1514.34089
Summary: This paper deals with the problem of the global uniform stability of nonlinear time-varying systems in the presence of perturbations. The main novelty relies on the fact that the proposed approach for stability analysis allows for the computation of the bounds which characterize the asymptotic convergence of solutions to a small ball centered at the origin. Therefore, we generalize some results which have already be announced in the literature. Furthermore, we provide a numerical example to validate the effectiveness of our main result.
MSC:
| 34D20 | Stability of solutions to ordinary differential equations |
| 37C60 | Nonautonomous smooth dynamical systems |
| 34D10 | Perturbations of ordinary differential equations |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
Keywords:
scalar differential equation; time-varying systems; uncertainties; Lyapunov function; global practical uniform stabilityReferences:
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