Pole placement through the modalator approach

This paper presents the derivation of the modalator that is defined as the (n-m)^th dynamic system that performs the modal analysis of the closed-loop system operating under a state feedback control law. Specifically, it is shown that when a system is operating under a state feedback control one can derive an (n-m)^th order dynamic system-termed a modulator-that has properties similar to the Luenberger observer with the exception that it does not require knowledge of the output. This independence of the dynamic behaviour from the output is due to the eigenvector subspace in which this dynamic behaviour evolves.