# Computation of the $\mathcal{L} \infty$ -norm of finite-dimensional linear systems

Abstract : In this paper, we study the problem of computing the $\mathcal{L}\infty$- norm of finite-dimensional linear time-invariant systems. This problem is first reduced to the computation of the maximal x-projection of the real solutions $(x, y)$ of a bivariate polynomial system $\sum=\{P,{\frac{\partial{P}}{\partial{y}}}\}$, with ${P} \in \mathbb{Z}[x, y]$. Then, we use standard computer algebra methods to solve the problem. In this paper, we alternatively study a method based on rational univariate representations, a method based on root separation, and finally a method first based on the sign variation of the leading coefficients of the signed subresultant sequence and then based on the identification of an isolating interval for the maximal $x$-projection of the real solutions of $\sum$.
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https://hal.inria.fr/hal-03328685
Contributor : Fabrice Rouillier Connect in order to contact the contributor
Submitted on : Monday, August 30, 2021 - 11:42:16 AM
Last modification on : Friday, August 5, 2022 - 11:59:57 AM

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Infinity_norm.pdf
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• HAL Id : hal-03328685, version 1

### Citation

Yacine Bouzidi, Alban Quadrat, Fabrice Rouillier, Grace Younes. Computation of the $\mathcal{L} \infty$ -norm of finite-dimensional linear systems. Communications in Computer and Information Science, Springer Verlag, 2021. ⟨hal-03328685⟩

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