Minimal Decoupling Indices for Linear Systems*

We show that for any right invertible linear system, there is a unique minimum list integers that represent the least expensive increases of infinite structure to produce for decoupling by non regular static state feedback, without changing the essential orders. In this case, this original list of minimal decoupling indices allows to establish necessary and sufficient conditions when the couplings between R* and the rest of the system do not affect the part that must change the structure at infinity, which is, to our knowledge, a second original contribution.