Feedback control of singular systems—proportional and derivative feedback of the state

This paper examines the use of proportional and derivative feedback of the state as a means of regularizing and controlling singular systems. Regularizability is defined as the existence of a derivative feedback control law such that the closed-loop system is regular. It is shown that the closed-loop system modal frequencies could be assigned arbitrarily if and only if the singular system is strongly controllable. It is further shown that, the eigenvalues of a regularizable system, could be assigned arbitrarily using the controllability property of finite frequency modes.