Innovations system representation in the optimal LQG regulation problem

New insights on the role of the innovations system representation in the context of the optimal LQG (H₂) ´standard´ problem are provided. The optimal controller is derived by using polynomial matrix techniques based on an innovations representation of the system. This can be obtained from the physical description by solving an appropriate minimum mean-square error filtering problem. The key result is that both the descriptions share the same optimal controller. A quite general cascade control structure is revisited in the present setting and the appropriate filtering problem is solved. The optimal controller is further obtained and the overall design procedure is compared with the one based on the physical system description. As a result, both a generalisation of the solution for the proposed cascade control problem and a better understanding of the role of the innovations system representation are provided.