Decoupling Controller Design for Linear Multivariable Plants

We study decoupling controller design for linear time-invariant square MIMO plants under unity feedback configuration. We show that if the plant has no coincidence of unstable poles and zeros, the necessary and sufficient condition for closed-loop stability can be simplified. The simplification leads to a simple characterization of the set of all achievable decoupled I/O maps and an algorithm which allows the design of decoupling controllers to achieve pre-assigned closed-loop poles.