Symmetric and non-symmetric controllers for symmetric systems

This paper is concerned with control of symmetric systems. The term "symmetric" means that the transfer function matrix describing a system is symmetric. For control of symmetric systems, it may seem suitable to use symmetric controllers. This paper shows in the context of H-infinity control that it is true if no constraint is imposed on the orders of controllers, but it is not true if the orders of controllers are specified to be lower than that of the system to be controlled.