On robustness analysis of linear vibrational control systems

By injecting high frequency dither signals, it is possible to stabilize an inverted pendulum without any feedback. The concept of the vibrational control system is thus proposed to provide extra design freedom in stabilization or other performance indexes. Although various vibrational control algorithms have been proposed and implemented in literature, little work has been done to show their robustness with respect to disturbances and uncertainties. This paper focuses on the robustness analysis of linear vibrational control systems with additive disturbances. By applying perturbation techniques, the linear vibrational control system is shown to be input-to-state stable with respect to disturbances. When disturbances are periodic, frequency analysis technique obtains a less conservative estimate of the ultimate bound of the system, indicating that disturbances with high frequencies lead to relatively small ultimate bounds. When additive state-dependent disturbances are considered, weak averaging techniques can be used to show the robustness of the system when bounded disturbances are slow time-varying. Numerical results support the theoretic analysis.