A frequency domain approach to the partial decoupling of non-minimum phase systems and non-decouplable systems

The problem of row-by-row decoupling by state feedback has been solved both in the time domain and in the frequency domain. Using the polynomial approach on the basis of co-prime matrix fraction descriptions, we here investigate the case, where a stable row-by-row decoupling is not possible. This may either be the case, when the system contains non-minimum phase zeros, or when the prerequisites for row-by-row decoupling are not fulfilled. A stable, but partial decoupling is then feasible by the introduction of a coupled row in the reference transfer matrix, where only one output is affected by several reference inputs. The design of this partial decoupling can be carried out in the frequency domain by an appropriate choice of the parametrizing polynomial matrices and subsequent solution of linear equations.