Symmetric systems can be transformed into uncoupled subsystems by using the group representation theory, which can reduce the computational effort required for Ｈ２ and Ｈ∞ control of the systems, especially for large scale systems whose controllers are synthesized directly for subsystems with lower dimensions. This paper presented several computational problems in Ｈ２ and Ｈ∞ controllers design to demonstrate the point that the use of symmetry can decrease the computational requirements, e.g. computation of control systems norm and solutions of Lyapunov equations and Riccati equations.