| In this thesis, the disturbance rejection problem for linear systems with control delays is researched. The contents of the research are as follows:1. The optimal vibration control for vehicle active suspension systems with controller delay is considered. The time delay for the controller is assumed as uncertain time-invariant but has a known constant bound. The dynamic models for the 2-degree-freedom quarter-car suspension system and the time domain model [1] for the road roughness stochastic power input are established. The control delay is transformed into an equivalent nondelayed one in form by the mode transformation. then according to the standards of road comfort and road holding the optimal state feedback vibration control law is designed, which can be obtained optimally through Riccati and Sylvester equations. The optimal vibration control law is proved to be unique. It is confirmed by the simulations that the designed controller can not only preserve the closed-loop stability in spite of the existence of the actuator time delay within allowed bound but achieve a better performance than the delay-independent controller.2. The H∞control for vehicle active suspension systems with controller delay is considered. The time delay for the actuator is assumed as uncertain time-invariant but has a known constant bound, and the dynamic models for the eight-degree-freedom full-car suspension system and the temporal model for the road roughness stochastic power input are established. Then, according to the standards of road comfort and road holding the elay-dependent memoryless state feedback H∞controller is designed, which can be obtained optimally through delay-dependent matrix inequalities. It is confirmed by the simulations that the designed controller can not only achieve the optimal performance for active suspensions but also preserve the closed-loop stability in spite of the existence of the actuator time delay within allowable bound.
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