On Topological Properties of the Set of Stabilizing Feedback Gains
Provides a theoretical foundation and practical algorithm for control engineers designing stabilizing feedback controllers.
This paper characterizes the topological structure of stabilizing feedback gains for SISO LTI systems, proving that the set of stabilizing output feedback gains has at most ceil(n/2) connected components, and provides an algorithm to determine stabilizing gain intervals and count unstable roots.
This work presents a fairly complete account on various topological and metrical aspects of feedback stabilization for single-input-single-output (SISO) continuous and discrete time linear-time-invariant (LTI) systems. In particular, we prove that the set of stabilizing output feedback gains for a SISO system with n states has at most $\lceil{\frac{n}{2}}\rceil$ connected components. Furthermore, our analysis yields an algorithm for determining intervals of stabilizing gains for general continuous and discrete LIT systems; the proposed algorithm also computes the number of unstable roots in each unstable interval. Along the way, we also make a number of observations on the set of stabilizing state feedback gains for MIMO systems.