On the stabilization of closed-loop stabilizable systems

The question of stabilizing unity feedback linear systems through the employment of proper feedforward compensators is important in many aspects of control theory. Although it appears to be well-known that a large class of linear systems, namely those which might be termed "closed-loop stabilizable," can be so stabilized, it is difficult to find a definitive reference which establishes this observation in a straightforward and simple manner. This note attempts to remedy this situation by presenting a new procedure for designing appropriate, proper, feedforward compensators which not only stabilize, but also arbitrarily reposition all of the unstable poles of closed-loop stabilizable systems.