Invariant spaces of linear systems: application to block decoupling

The authors solve the dynamic-state-feedback block-decoupling problem in the general case, i.e. with singular or nonsingular input transformations. They prove that the problem is solvable if the number of inputs is large enough. The main tools for this study are some invariant spaces associated with the columns infinite behavior of a rotational matrix. It turns out that when the problem is solvable, it is also solvable with stability