On Topological Properties of the Set of Stabilizing Feedback Gains

This article presents a fairly complete account on various topological and metrical aspects of feedback stabilization for single-input single-output (SISO) continuous discrete time linear time-invariant (LTI) systems. In particular, we prove that the set stabilizing output gains SISO system with n states have at most [n/2] connected components. Furthermore, our analysis yields an algorithm determining intervals general LTI systems; proposed also computes number unstable roots in each interval.