${cal L}_{\infty }$ -Norm Computation for Continuous-Time Descriptor Systems Using Structured Matrix Pencils

In this technical note, we discuss an algorithm for the computation of the L_∞-norm of transfer functions related to descriptor systems. We show how one can achieve this goal by computing the eigenvalues of certain skew-Hamiltonian/Hamiltonian matrix pencils and analyze arising problems. We also formulate and prove a theoretical result which serves as a basis for testing a transfer function matrix for properness. Finally, we illustrate our results using a descriptor system related to mechanical engineering.