Partial model matching via static feedback (the multivariable case)

The problem of partial model matching is studied for the case of multi-input/multi-output (MIMO) linear time-invariant systems. Using a regular static state feedback law, the necessary and sufficient conditions for the problem to have a solution are established, the general analytic expressions of the controller matrices are derived. For the case of single-input/single-output systems sufficient conditions are derived for the solution of the partial model matching problem with simultaneous stabilizability. For the same type of systems the necessary and sufficient conditions for the solution of the partial model matching problem with simultaneous regulation of the free response of the closed loop system are established. Finally, the problem of partial model matching, via regular static measurement output feedback, is solved for the case of MIMO systems.