Robustness of Nonlinear Vibrational Control Systems based on Sampling Lyapunov Method

Abstract

Vibrational control algorithms have been shown their potential in achieving stability and improving the performance of engineering systems by injecting high-frequency dither signals. This paper presents the robustness analysis of nonlinear vibrational control systems while disturbances exist. The linearization matrix of the averaged system is assumed to be Hurwitz such that the nonlinear vibrational control system is vibrationally stabilizable without disturbances. In the presence of disturbances, the domain of attraction can be estimated by constructing a quadratic Lyapunov function, which provides an upper bound of disturbances that the system can handle. For all initial points from the do..