Robustness of Nonlinear Vibrational Control Systems based on Sampling Lyapunov Method

Xiaoxiao Cheng, Ying Tan, Iven Mareels

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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 domain of attraction, all disturbances constrained within the estimated bound, a Lyapunov-based sampling method is applied to show that the solutions converge to an ultimate bound, which is a function of the bound of disturbances. That indicates the stabilized vibrational control systems are robust to a class of additive and bounded disturbances. As an illustrative example, an inverted pendulum stabilized by the vibrational control algorithm is shown to have the ability to track a vertically moving target without a feedback, in which moving speed is regarded as a disturbance. Numerical results support the theoretic findings.

Original languageEnglish
Title of host publication2018 Annual American Control Conference, ACC 2018
Number of pages6
ISBN (Print)9781538654286
Publication statusPublished - 9 Aug 2018
Event2018 Annual American Control Conference, ACC 2018 - Milwauke, United States
Duration: 27 Jun 201829 Jun 2018

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Conference2018 Annual American Control Conference, ACC 2018
Country/TerritoryUnited States


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