This paper offers with the theoretical and computational evaluation of optimal& robust controlproblems, with the goal of providing answers to them with MATLAB simulation.For the robust control,  -synthesis controller and for the optimal control, LQR controller are designed for a quarter car active suspension system to maximize the ride comfort and road handling criteria’s of the vehicle. The proposed controllers are designed using Matlab script program using time domain analysis for the four road disturbances (bump, random sine pavement and (...) white noise) for the control targets suspension deflection, body acceleration and body travel. Finally the simulation result proves the effectiveness of the active suspension system with  -synthesis controller. (shrink)