On non-local vibrational stabilization of nonlinear systems

This paper focuses on showing non-local vibrational stabilization of a general class of nonlinear vibrational control systems. Instead of using the linearization of the averaged system to conclude the local vibrational stability, a new concept of semi-global practical vibrational stability is proposed. Our main result shows that if the averaged system is uniformly globally asymptotically stable, the nonlinear vibrational control system is semi-globally practically vibrationally stable. The desired domain of attraction and the ultimate bound of the nonlinear vibrational control system can be achieved by tuning the parameter ϵ. Furthermore, this new definition makes it possible to analyze the robustness of nonlinear vibrational control systems. A simulation example is presented to illustrate our results.