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Electrical Engineering and Systems Science > Systems and Control

arXiv:2108.00728 (eess)
[Submitted on 2 Aug 2021 (v1), last revised 23 Sep 2021 (this version, v2)]

Title:Complexity of the LTI system trajectory boundedness problem

Authors:Guillaume O. Berger, Raphaël M. Jungers
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Abstract:We study the algorithmic complexity of the problem of deciding whether a Linear Time Invariant dynamical system with rational coefficients has bounded trajectories. Despite its ubiquitous and elementary nature in Systems and Control, it turns out that this question is quite intricate, and, to the best of our knowledge, unsolved in the literature. We show that classical tools, such as Gaussian Elimination, the Routh--Hurwitz Criterion, and the Euclidean Algorithm for GCD of polynomials indeed allow for an algorithm that is polynomial in the bit size of the instance. However, all these tools have to be implemented with care, and in a non-standard way, which relies on an advanced analysis.
Comments: To appear in Proceedings of 2021 60th IEEE Conference on Decision and Control (CDC)
Subjects: Systems and Control (eess.SY)
Cite as: arXiv:2108.00728 [eess.SY]
  (or arXiv:2108.00728v2 [eess.SY] for this version)
  https://doi.org/10.48550/arXiv.2108.00728

Submission history

From: Guillaume O. Berger [view email]
[v1] Mon, 2 Aug 2021 08:55:16 UTC (328 KB)
[v2] Thu, 23 Sep 2021 09:09:05 UTC (342 KB)
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