This dissertation, "Control of Vehicle Suspension Systems and Its Extension to General Vibration Systems" by Panshuo, Li, 李攀碩, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: This thesis is concerned with the vibration attenuation problem of vehicle suspension systems and its extension to general vibration systems. Two research themes are considered: control methods for vehicle suspension systems and stability, performance analysis, and controller design for periodic piecewise linear systems. For vehicle suspension, control methods are proposed in order to improve ride quality, ensure ride safety and avoid structural damage. First, an adaptive suspension is designed with adjustable inerter, which can adaptively adjust its inertance. An H2 controller aiming at improving the suspension performances is designed to formulate the objective control input. The adjustable inerter adaptively varies its inertance under control to track this objective. Since the inerter cannot exert force to the system, which results in sub-optimal suspension performance, an active suspension with wheelbase preview is designed to enhance the performances. A multi-objective schme aiming at improving ride quality as far as possible subject to acceptable ride safety, avoiding structural damage and actuator saturation, is proposed for a half-car vehicle suspension model. Static output-feedback control is considered from an implementation point of view and an algorithm is presented to obtain the controller gain. Considering that the vehicle velocity may be uncertain or time-varying in practice, a multi-objective velocity-dependent controller is designed as an improved scheme. To treat the velocity as uncertainty or a time-varying parameter, robust controllers developed using homogeneous polynomial parameter-dependent approach and linear parameter-varying approach are proposed. Finally, a more realistic nonlinear full-car system with unknown dynamics characteristics is considered. Based on the successful application on a quarter-car test rig with active disturbance rejection control (ADRC), motion based ADRC is proposed to stabilize the vehicle body of the full-car model. Full-car dynamics are extracted as three interconnected subsystems, considering the heave, pitch, and roll motions. For each subsystem, an extended state observer is established to observe the total disturbance which captures the unknown internal dynamics and external excitation. A PD / Fuzzy-PD controller is constructed for the subsystem after compensating the total disturbance. Four actuator inputs are obtained in real time according to the three motion based controller outputs. For periodic piecewise linear systems, stability, stabilization, performance indices and controller design problems are investigated. First, two sufficient, and one necessary conditions concerning the exponential stability of periodic piecewise linear system with possibly non-Hurwitz subsystems are proposed. To facilitate the performance analysis and controller synthesis, a stability condition is established by employing continuous time-varying Lyapunov function. Based on the stability result, L2-gain and generalized H2 performance criteria are developed as well. By considering a more general formulation of Lyapunov function, that is, discontinuous Lyapunov function with time-varying Lyapunov matrix, stability, stabilization and L2-gain performance are studied by allowing the proposed Lypuanov function to be possibly non-monotonically decreasing over a period. A corresponding algorithm for the stabilizing controller is presented t