Commutativity of Systems with their Feedback Conjugates

Abstract: After introducing commutativity concept and summarizing the relevant literature, this work is focused on the commutativity of feedback conjugates. It is already known that a linear time-varying differential system describing a single input-single output dynamical system is always commutative with its constant gain feedback pairs. In this article, it is proven that among the time-varying feedback conjugates of a linear time-varying system, constant feedback conjugates are the only commutative feedback pairs and any of the time-varying feedback conjugates cannot constitutes a commutative pair of a linear time-varying system.