The optimal projection equations for fixed-structure decentralized dynamic compensation

The optimal projection equations for quadratically optimal fixed-order (centralized) dynamic compensation obtained in [5] are generalized to the case in which the dynamic compensator has, in addition, a fixed decentralized structure. Under a stabilizability assumption for the particular feedback configuration, the resulting optimality conditions provide the insight that each subcontroller must possess an internal model of not only the controlled plant but also of all other subcontrollers. This form of the solution provides insight into the mechanism by which the fixed-structure assumption resolves the difficulty of the "second guessing" phenomenon discussed in [1].