This paper deals with the observer based robust control design problem for multivariable laboratory process with time-varying uncertain parameters. By using the Young relation, and the cone-complementary, the stabilization problem is then converted into convex optimization one with LMI constraints. PDC controller and observer gains are obtained under L-2-bounded disturbance by set feasible solutions of LMI conditions. The effectiveness of the proposed design methodology is illustrated by considering a Quadruple-tank systems. This paper deals with the observer based robust control design problem for multivariable laboratory process with time-varying uncertain parameters. By using the Young relation, and the cone-complementary, the stabilization problem is then converted into convex optimization one with LMI constraints. PDC controller and observer gains are obtained under L-2-bounded disturbance by set feasible solutions of LMI conditions. The effectiveness of the proposed design methodology is illustrated by considering a Quadruple-tank systems.