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Journal Articles Communications in Computer and Information Science Year : 2021

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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Dates and versions

hal-03328685 , version 1 (30-08-2021)

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Cite

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, 2021, Communications in Computer and Information Science, 1414, pp.119-136. ⟨10.1007/978-3-030-81698-8_9⟩. ⟨hal-03328685⟩
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