On the Relative Gain Array (RGA) with Singular and Rectangular Matrices
This work addresses a methodological gap for control engineers applying RGA to singular or rectangular systems, but the contribution is incremental.
The paper identifies a deficiency in using the Moore-Penrose pseudoinverse for the Relative Gain Array (RGA) with singular matrices, showing it fails to preserve critical properties, and proposes an alternative generalized inverse to preserve them.
In this paper we identify a significant deficiency in the literature on the application of the Relative Gain Array (RGA) formalism in the case of singular matrices. Specifically, we show that the conventional use of the Moore-Penrose pseudoinverse is inappropriate because it fails to preserve critical properties that can be assumed in the nonsingular case. We then discuss how such properties can be rigorously preserved using an alternative generalized matrix inverse.