A note on balanced controller reduction

The standard linear quadratic Gaussian (LQG) optimal controller is not minimal in general, even if the plant is minimal. Hence, the order of the optimal controller can be less than that of the plant. This note shows that the original balancing method of Moore [1] can be used to generate these reduced order optimal controllers, but the newer balancing methods recently proposed for controller reduction might not generate the reduced order optimal controllers, even when they exist.