Relative Gain Array for Norm-Bounded Uncertain Systems

This paper considers the extension of relative gain array (RGA) to norm-bounded uncertain systems. We present a method for calculating a tight bound on the worst-case relative gain and derive necessary and sufficient conditions for the sign change of the relative gain over the uncertainty set. The proposed results improve on recently published results [Chen and Seborg, AIChE J. 2002, 48, 302]. More importantly, it is shown that the role of RGA is limited for ascertaining the integrity of uncertain systems. This conclusion is in direct contrast with the corresponding result for adjudging integrity of nominal systems, where the usefulness of RGA is well-known. As an offshoot, we present a signal-based representation of the relative gain for uncertain systems.