Academic Journal
${L}^{\infty}$-norm computation for linear time-invariant systems depending on parameters
| العنوان: | ${L}^{\infty}$-norm computation for linear time-invariant systems depending on parameters |
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| المؤلفون: | Quadrat, Alban, Rouillier, Fabrice, Younes, Grace |
| المساهمون: | OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs (OURAGAN), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Sorbonne University Abu Dhabi (SUAD), SUAD_SAFIR |
| المصدر: | EISSN: 2564-3029 ; Maple Transactions ; https://inria.hal.science/hal-04646145 ; Maple Transactions, 2024, 4 (1), pp.18. ⟨10.5206/mt.v4i1.17129⟩ |
| بيانات النشر: | CCSD Western Libraries Western University |
| سنة النشر: | 2024 |
| مصطلحات موضوعية: | Computer Algebra, Control theory, Computing methodologies, Algebraic algorithms, Polynomial systems, $L^{\infty}$-norm computation, [INFO]Computer Science [cs], [MATH]Mathematics [math] |
| الوصف: | International audience ; 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.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. 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. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| Relation: | info:eu-repo/semantics/altIdentifier/arxiv/2312.00760; ARXIV: 2312.00760 |
| DOI: | 10.5206/mt.v4i1.17129 |
| الاتاحة: | https://inria.hal.science/hal-04646145 https://inria.hal.science/hal-04646145v1/document https://inria.hal.science/hal-04646145v1/file/LinfinityMTstyle.pdf https://doi.org/10.5206/mt.v4i1.17129 |
| Rights: | http://creativecommons.org/licenses/by/ ; info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.F102471A |
| قاعدة البيانات: | BASE |
| DOI: | 10.5206/mt.v4i1.17129 |
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