# Abstract:

The aim of this paper is to propose a new contribution in the domain of the famous Decoupling Problem for Linear Time-Invariant systems: we introduce here and solve the so-called $k$th-order Partial Non Interacting Problem (PNIP($k$)), which amounts to diagonalizing the first $k$ Markov parameters of the compensated plant. This contribution is based on classical results on exact decoupling and the partial treatment is inspired from a similar control problem, namely the partial model matching problem.

# Classification:

93B11, 93C05, 93B52, 93B50, 93B27