Asymptotic and Probabilistic Perturbation Analysis of Controllable Subspaces

Vera Angelova Angelova; Mihail Konstantinov; Petko Petkov

doi:10.20944/preprints202411.0022.v1

Preprint Article Version 1 This version is not peer-reviewed

Version 1 : Received: 31 October 2024 / Approved: 31 October 2024 / Online: 1 November 2024 (13:55:50 CET)

In this paper, we consider the sensitivity of the controllable subspaces of single-input linear control systems to small perturbations of the system matrices. The analysis is based on the strict componentwise asymptotic bounds for the matrix of the orthogonal transformation to canonical form, derived by the method of the splitting operators. The asymptotic bounds are used to obtain probabilistic bounds on the angles between perturbed and unperturbed controllable subspaces implementing the Markoff inequality. It is demonstrated that the probability bounds allow to obtain sensitivity estimates which are much tighter than the usual deterministic bounds. The analysis is illustrated by a high order example.

perturbation analysis; controllable subspaces; linear control systems; probabilistic bounds

Computer Science and Mathematics, Computational Mathematics

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Asymptotic and Probabilistic Perturbation Analysis of Controllable Subspaces

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