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arXiv · 1904.08451

On Topological Properties of the Set of Stabilizing Feedback Gains

Jingjing Bu·Afshin Mesbahi·Mehran Mesbahi
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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 $\lceil{\frac{n}{2}}\rceil$ 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.

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Jingjing Bu, Afshin Mesbahi, Mehran Mesbahi. 2019-04-17. On Topological Properties of the Set of Stabilizing Feedback Gains. https://arxiv.org/abs/1904.08451

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