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

Linear multivariable systems are studied under the unity-feedback configuration. For plants with no coincidences of unstable poles and zeros, the authors prove a simplified condition for closed-loop stability. The simplification leads to a simple description of the set of all achievable input/output (I/O) maps and a simple parametrization of all controllers achieving the same I/O map. The results are used to study decoupling controller design for nonsquare unstable plants. They describe the set of all achievable decoupled I/O maps and prove a necessary and sufficient condition for the existence of stable decoupling controllers. Computationally simple algorithms for the design of decoupling controllers to achieve preassigned closed-loop poles and zeros are proposed