({L}^{\infty}\)-norm computation for linear time-invariant systems depending on parameters

This paper focuses on representing the \(L^{\infty}\)-norm of finite-dimensional linear time-invariant systems with parameter-dependent coefficients. Previous studies tackled the problem in a non-parametric scenario by simplifying it to finding the maximum \(y\)-projection of real solutions \((x, y)...

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Bibliographic Details
Published in:arXiv.org 2023-12
Main Authors: Quadrat, Alban, Rouillier, Fabrice, Younes, Grace
Format: Article
Language:English
Subjects:
Computer algebra
Parameters
Time invariant systems
Online Access:Get full text
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Summary:This paper focuses on representing the \(L^{\infty}\)-norm of finite-dimensional linear time-invariant systems with parameter-dependent coefficients. Previous studies tackled the problem in a non-parametric scenario by simplifying it to finding the maximum \(y\)-projection of real solutions \((x, y)\) of a system of the form \(\Sigma=\{P=0, \, \partial P/\partial x=0\}\), where \(P \in \Z[x, y]\). To solve this problem, standard computer algebra methods were employed and analyzed \cite{bouzidi2021computation}. In this paper, we extend our approach to address the parametric case. We aim to represent the "maximal" \(y\)-projection of real solutions of \(\Sigma\) as a function of the given parameters. %a set of parameters \(\alpha\). To accomplish this, we utilize cylindrical algebraic decomposition. This method allows us to determine the desired value as a function of the parameters within specific regions of parameter space.
ISSN:2331-8422