Matrix fraction description approach to decentralised control

A two-channel linear system ¿¿ is given, defined by its transfer matrix G(s), for which a (right) matrix fraction description in the form G(s) = R(s) P¿¿1 (S) is also provided. Local output feedbacks of the form ui = ¿¿ Kiyi are considered, and their effect on the system ¿¿ is studied via the so-called D-controllability problem. This problem is solved using the above definition of ¿¿, and a simple criterion for its solvability is presented involving suitable submatrices of R(S) and P(S). Finally, some results concerning the decentralised stabilisability problem, and the connection to decentralised fixed modes, are also given.