Work

Asymptotic and Probabilistic Perturbation Analysis of Controllable Subspaces

Year: 2024

Type: article

Abstract: 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.

Source: Computation

DOI: 10.3390/computation12120236

Authors: Vera Angelova Angelova, Mihail Konstantinov, Petko Petkov

Institutions: Bulgarian Academy of Sciences, Institute of Information and Communication Technologies, University of Architecture, Civil Engineering and Geodesy

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,046

OpenAlex ID: W4404819624

FWCI:

Cites: 26

Cited by:

Related to: 10