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

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Yacine Bouzidi
• Function : Author
• PersonId : 955292
• Function : Author
• PersonId : 833444
Fabrice Rouillier
Grace Younes

#### 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.

### Dates and versions

hal-03073801 , version 1 (16-12-2020)

### Identifiers

• HAL Id : hal-03073801 , version 1

### Cite

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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