On Topological Properties of the Set of Stabilizing Feedback Gains

Authors

Jingjing Bu, Afshin Mesbahi, Mehran Mesbahi

Year

2019

Journal Paper

Source

IEEE Transactions on Automatic Control

Identifiers

arXiv 1904.08451 DOI 10.1109/tac.2020.2992510

Abstract¶

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 lceiln/2rceil 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.