ON INTERACTION INDICATORS FOR MULTIVARIABLE SYSTEMS

A number of relationships between some indicators of interaction in multivariable systems is presented, with particular reference to two-input two-output systems. It is shown that for real 2 x 2 matrices, the regions of the gain space identified using the generalized diagonal dominant (g.d.d.) and Ostrowski criteria are identical. It is further shown that almost all 2 x 2 matrices either are g.d.d., or can be rendered g.d.d. by a row or a column exchange. A critical quantity in developing the above relationships is the multivariable structure index, as used in 'relative gain array' analysis and, more recently, in the 'individual channel analysis' method. Finally it is shown that knowledge of the eigenstructure of a complex n x n matrix allows a new version of Gershgorin's theorem to be stated using circles of smaller radii if the misalignment angles are less than 45-degrees.