Robust and Efficient Algorithms for ℒ∞-Norm Computation for Descriptor Systems

In this paper we discuss algorithms for the computation of the ℒ∞-norm of transfer functions related to descriptor systems, both in the continuous- and discrete-time context. We show how one can achieve this goal by computing the eigenvalues of certain structured matrix pencils. These pencils can be transformed to skew-Hamiltonian/Hamiltonian matrix pencils which are constructed by only using the original data. Furthermore, we apply a structure-preserving algorithm to compute the desired eigenvalues. In this way we increase robustness and efficiency of the method. Finally, we present numerical results in order to illustrate the advantages of our approach.