A note on gramian-based interaction measures

Abstract

This note deals with the choice of measurement/actuator pairs for decentralized control, where the controller remains unspecified. The theoretical background of gramian based interaction measures is clarified and a geometrical interpretation is given. Moreover, a generalization of the Hankel interaction index array is proposed and it is shown that the introduction of weighted gramians makes the criteria more flexible compared to the augmenting with additional filter dynamics.