Asymptotic behavior of solutions of a class of time-varying systems with periodic perturbation

Abstract

This paper deals with stability of nonlinear differential equations with parameter with periodic perturbation. We determine values of the parameter under which the solutions of the perturbed systems could be uniformly exponentially stable. Sufficient conditions for global uniform asymptotic stability and/or practical stability in terms of Lyapunov-like functions are obtained in the sense that the trajectories converge to a small ball centered at the origin. Moreover, to illustrate the applicability of our result, we study the stabilization problem for a class of control system.