Robustness and Dynamic Interaction

Abstract

The article addresses the dynamic interaction of a perturbed multivariable process under control and the systematic reduction of the interaction. As a basis, gradient-oriented steps of the controller are used. The influence of spherical uncertainties is included as the main issue. The controllability Gramian operates for analyzing the interaction, i.e., the interaction is expressed in terms of the energy of selected outputs when the system is excited by selected input impulses. For a given upper bound of the Frobenius norm of the uncertainties, the structural details of their maximum influence is determined. A special type of a selection matrix is defined for the main step in the analytical derivation. Both continuous-time and discrete-time problems, large-scale and small uncertainties are taken into consideration.