Vous trouverez ici toutes les informations relatives à la soutenance de thèse de Grace Younes.
La date : Jeudi 20 Janvier 2022 à 13:30
La salle : 15-16-413
La visio : salon spécial sur le serveur de visio d’OURAGAN
Le streaming : Chaine twitch DéMATHérialisation
Computation of the L-infinity-norm of finite-dimensional linear systems
Abstract : In this dissertation, we study the computation of the L∞-norm of finite-dimensional linear time-invariant systems. This problem is first reduced to the computation of the maximal y-projection of the real solutions (x, y) of a bivariate polynomial equations system Σ = {P = 0, ∂P/∂x = 0}, where P ∈ Z[x, y]. Then, we use standard computer algebra methods to solve this problem. In particular, 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 a signed subresultant sequence (Sturm-Habicht) and on the identification of an isolating interval for the maximal y-projection of the real solutions of Σ. We then compute the worst-case bit complexity of each method and compare their theoretical behavior. We also implement each method in Maple and compare their practical behavior (average complexity). A generalization of the above algorithms is finally proposed to the case where the polynomial P also depends on a set of parameters α = [α1,…, αd] ∈ R^d. To do that, we solve the problem using the notion of the Cylindrical Algebraic Decomposition, well-known in algebraic geometry.
