On the regularizability of singular systems

The property of regularity of singular systems is not a feedback invariant. To correct this deficiency a new property of regularizability is defined and geometric tests are given for it in terms of system matrices. Regularizability is shown to be the natural extension of regularity, which is a condition on the homogeneous system, to controlled singular systems. Definitions of controllability and reachability are modified depending on regularizability rather than regularity. A brief comparison of proportional and proportional-plus-derivative feedback laws in the context of making the closed-loop system regular, regular and reachable, and regular and controllable is also given. Dynamical interpretations of these properties are also presented