Descriptive vector, relative error matrix, and interaction analysis of multivariable plants

In this paper, we introduce a vector which is able to describe the Niederlinski Index (NI), Relative Gain array (RGA), and the characteristic equation of the relative error matrix. The spectral radius and the structured singular value of the relative error matrix are investigated. The cases where the perfect result of the Relative Gain Array, equal to the identity matrix, coincides with the least interaction in a plant are pointed out. Then, the Jury Algorithm is adopted to get some insight into interaction analysis of multivariable plants. In particular, for interaction analysis of 3×3 plants, simple yet promising conditions in terms of the Relative Gain Array and the NiederLinski Index are derived. Several examples are also discussed to illustrate the main points.