Computation of the L∞-norm of finite-dimensional linear systems
Résumé
In this paper, we study the computation of the L∞-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 {P,∂P∂y}⊂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.