Analysis for non-strictly-proper systems

We consider feedback systems where the plant and compensator are governed by arbitrary rational matrices. Several conventional methods of closed-loop stability analysis are examined. These include state-space theory, rational matrix analysis, Q-parametrization, and singular system theory. We show that existing methods are inadequate to fully characterize closed-loop stability when non-strictly-proper systems are involved. Our analysis establishes a simple necessary condition under which the closed-loop system is stable. Our condition is then applied to refine the existing methods