Computation of the L∞ -norm of finite-dimensional linear systems
Résumé
In this paper, we study the problem of computing the L∞- 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 ∑={P,∂P∂y}, with P∈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 ∑.
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