${\cal L}_{\infty}$-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.

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