The solution of diagonal decoupling problem by dynamic output feedback and constant precompensator: the general case

In this paper, the solution to diagonal decoupling problem via dynamic output feedback and constant precompensator is presented in the general case. The literature contains a number of particular solutions for this problem. These solutions are valid, for instance, for square transfer matrices or they employ restricted dynamic output feedback schemes. Here, we start with a nonsquare transfer matrix and consider a dynamic output feedback scheme where there is a proper compensator in the feedback loop accompanied by a constant gain (precompensator) in the feedforward path. In this respect, the problem being considered is the dynamic output feedback version of the well-known Morgan´s problem. The approach taken involves the characterization of open-loop diagonalizers which admit a dynamic output feedback realization. The key concepts involved in the solution are the generalized version of diagonal causality degree dominance and the set of attainable infinite zero orders. An example is also included to illustrate the main result