A unifying approach to the decoupling of linear multivariate systems

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Abstract
A unifying approach to the decoupling problem (diagonal, triangular, block decoupling) is introduced. The key element is the interactor, a polynomial matrix of unique structure associated with the transfer matrix of the system. Necessary and sufficient conditions for block decoupling are derived and the stability questions are resolved using the block coupling zeros. The results obtained (for decoupling via state feedback, state feedback plus input dynamics and constant output feedback) are conceptually simple, unify and expand those existing, and easily lead to constructive decoupling algorithms.