Measurement of interactions in multivariable systems: some structural issues

This paper is concerned with some structural aspects of interaction measurements in multivariable systems. The authors pose a decentralized control problem regarding the independent design of local controllers to achieve closed-loop stability both in the subsystem levels and in the overall interconnected system. That problem and its variations in the literature are generally solvable if the interaction dynamics are negligibly small. In this paper, precise solvability conditions for the problem are given for a large class of systems and how the pole/zero structure of a system plays a fundamental role in the effectiveness of interactions between its control channels is explicitly shown. It is argued that the classical interaction measures which are based on the evaluation of frequency response characteristics of the channel interactions, although useful in some instances, are generally incapable of giving a correct evaluation of interaction dynamics especially when extra unstable poles and zeros are introduced to the system through the interconnections.