On the class of all stabilizing controllers

This paper shows that the class of all strictly proper stabilizing controllers for proper linear plants can be structured as state estimate feedback with frequency shaping in the state estimates and/or in the state estimate feedback law. The selection of where the frequency shaping takes place is at the designers discretion. The parameterization of the controller class can be in terms of an arbitrary proper stable transfer function, with the closed loop system transfer functions affine in this transfer function. With constant output feedback permitted in addition to the state estimate feedback, the class of all proper stabilizing controllers can be generated in like manner.