ln the present work, linear optimal control theory is applied to the design of active suspension systems for automobiles. Most of the effort is directed towards the case of the half-car model problem in which the correlation between front and rear wheel inputs is taken into consideration. Particular attention is focussed on the difference between the optimal correlated and uncorrelated cases. To this end, rigorous mathematical developments are considered. An optimal control law for a vehicle suspension is developed using a discrete regulator framework. The time delay between the disturbance due to the road at the leading and trailing wheels is incorporated, without approximation, into the model. The control law derived for the optimal correlated problem requires information gathered at the leading wheel. The superiority of this solution over the suboptimal one, which does not incorporate leading wheel information, is clearly confirmed by the computer simulation. To enhance the performance of active suspension systems, under preview of the road, the application of linear optimal control theory is also considered. The vehicle model with completely general inputs to front and rear wheels is set up as an optimization problem and it is converted to standard form by a state variable transformation. It is shown that the solution for the optimal tracking problem over a finite time interval is not of practical use, because it requires knowledge of the road surface over the whole joumey time, whereas for a preview control scheme, a sensor mounted on a car in motion would provide a continuously moving window of road surface data. By combining linear optimal theory with ideas for the overtaking optimality method, controllaws for both infinite and finite preview problems are produced. The solution obtained in this framework utilizes road surface data in precisely the format which would be available from a preview sensor. The discrete time version of this solution is also examined. ln the simulationon either processing or actuator speeds, the value of preview in enhancing quarter and half-car suspension performances is assessed as a function of preview time and the simulation results show clear benefits are possible when the future road information is included.