Approximate Stability Radius Analysis and Design in Linear Systems

The robustness of the stability properties of dynamical systems in the presence of unknown/adversarial perturbations to system parameters is a desirable property. In this paper, we present methods to efficiently compute and improve the approximate stability radius of linear time-invariant systems. W...

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Bibliographic Details
Published in:arXiv.org 2024-03
Main Authors: Rai, Ananta Kant, Katewa, Vaibhav
Format: Article
Language:English
Subjects:
Dynamic stability
Dynamical systems
Linear systems
Robustness (mathematics)
Stability analysis
Time invariant systems
Online Access:Get full text
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Summary:The robustness of the stability properties of dynamical systems in the presence of unknown/adversarial perturbations to system parameters is a desirable property. In this paper, we present methods to efficiently compute and improve the approximate stability radius of linear time-invariant systems. We propose two methods to derive closed-form expressions of approximate stability radius, and use these to re-design the system matrix to increase the stability radius. Our numerical studies show that the approximations work well and are able to improve the robustness of the stability of the system.
ISSN:2331-8422