Stabilization, parameterization, and decoupling controller design for linear multivariable systems

The authors study linear multivariable systems under the unity-feedback configuration. For nonsquare plants with no coincidence of unstable poles and zeros, they prove a simplified condition for closed-loop stability. The simplification leads to a simple description of the set of all achievable I/O maps and a single parameterization of all controllers achieving the same I/O map. The results are used to describe the set of all achievable decoupled I/O maps and prove a necessary and sufficient condition for the existence of stable decoupling controllers