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

Abstract : In this paper, we study the computation of the $\mathcal{L}_{\infty}$-norm for finite-dimensional linear 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 $\{\mathcal{P},\frac{\partial \mathcal{P}}{\partial y}\} \subset \mathbb{Z}[x,y]$. We then apply computer algebra methods to solve the problem. We alternatively study a method based on rational univariate representations, a method based on root separation, and finally a method based on the sign variation of the leading coefficients of the signed subresultant sequence and on the identification of an isolating interval for the maximal $x$-projection of the real solutions of the system.
Document type :
Conference papers
Domain :

https://hal.inria.fr/hal-03073801
Submitted on : Wednesday, December 16, 2020 - 11:51:36 AM
Last modification on : Saturday, December 19, 2020 - 3:38:59 AM

### Identifiers

• HAL Id : hal-03073801, version 1

### Citation

Yacine Bouzidi, Alban Quadrat, Fabrice Rouillier, Grace Younes. Computation of the $\mathcal{L}_{\infty}$-norm of finite-dimensional linear systems. Maple Conference, Nov 2020, Waterloo, Canada. ⟨hal-03073801⟩

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