Commutativity of Systems with their Feedback Conjugates

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 timevarying 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.