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arXiv · 1904.02737

On Topological and Metrical Properties of Stabilizing Feedback Gains: the MIMO Case

Jingjing Bu·Afshin Mesbahi·Mehran Mesbahi
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Abstract

In this paper, we discuss various topological and metrical aspects of the set of stabilizing static feedback gains for multiple-input-multiple-output (MIMO) linear-time-invariant (LTI) systems, in both continuous and discrete-time. Recently, connectivity properties of this set (for continuous time) have been reported in the literature, along with a discussion on how this connectivity is affected by restricting the feedback gain to linear subspaces. We show that analogous to the continuous-time case, one can construct instances where the set of stabilizing feedback gains for discrete time LTI systems has exponentially many connected components.

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Jingjing Bu, Afshin Mesbahi, Mehran Mesbahi. 2019-04-04. On Topological and Metrical Properties of Stabilizing Feedback Gains: the MIMO Case. https://arxiv.org/abs/1904.02737

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