New input-output pairing based on eigenvalue contribution measures

In this paper, a new approach based on the concept of combined controllability and observability is proposed to quantify the interaction among the inputs and outputs of both stable and unstable linear multivariable systems. The proposed approach computes the contribution of the system eigenvalues in the outputs and formulates a Relative Contribution Array (RCA) to quantify the input-output interactions and select the most appropriate set of input-output pairs. The proposed approach has many advantages over existing well known approaches, which are illustrated through a widely reported numerical example of a chemical process where conventional RGA is shown to lead to improper pairings while the proposed approach leads to far more accurate assessment of interaction.