Stability analysis of inerter-based n-DOF vibration systems containing semi-active switched elements

This paper investigates the stability problem of inerter-based semi-active n-degree-of-freedom (n-DOF) vibration systems containing semi-active switched elements, where the results can be applied to the design of many vibration control systems, such as building vibrations, vehicle suspensions, isolators, etc. Since introducing switched elements to n-DOF vibration systems may lead to instability, it is theoretically and practically meaningful to investigate the stability of n-DOF vibration systems containing semi-active switched elements. Necessary and sufficient conditions for the global asymptotic stability of a single-degree-of-freedom (SDOF) system containing at most one switched spring, one switched inerter, and one switched damper are derived, by solving the explicit solutions of the system states and analyzing the properties of energy functions. Based on the Lyapunov approach, a series of asymptotic stability conditions for the multi-degree-of-freedom (MDOF) system containing one semi-active switched inerter or one semi-active switched spring are derived. Finally, numerical simulation examples are presented to illustrate the stability results.