2023/12/01 by Alban Quadrat, Quadrat, Alban, Fabrice Rouillier +3 · 2 citations
Engineering · #Advanced Control Systems Optimization #Control Systems and Identification #FOS: Computer and information sciences #Stability and Control of Uncertain Systems #Symbolic Computation (cs.SC)
paper · pdf · doi:10.48550/arxiv.2312.00760
openalex publication_date 2023/12/01 · openalex created_date 2023/12/06 · openalex updated_date 2026/07/28
This paper focuses on representing the L∞-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 Σ=\P=0, ∂ P/∂ x=0\, where P ∈ \Z[x, y]. To solve this problem, standard computer algebra methods were employed and analyzed \citebouzidi2021computation. In this paper, we extend our approach to address the parametric case. We aim to represent the "maximal" y-projection of real solutions of Σ as a function of the given parameters. %a set of parameters α. 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.