TY - GEN A1 - Alam, Rafik A1 - Bora, Shreemayee A1 - Karow, Michael A1 - Mehrmann, Volker A1 - Moro, Julio T1 - Perturbation theory for Hamiltonian matrices and the distance to bounded-realness N2 - Motivated by the analysis of passive control systems, we undertake a detailed perturbation analysis of Hamiltonian matrices that have eigenvalues on the imaginary axis. We construct minimal Hamiltonian perturbations that move and coalesce eigenvalues of opposite sign characteristic to form multiple eigenvalues with mixed sign characteristics, which are then moved from the imaginary axis to specific locations in the complex plane by small Hamiltonian perturbations. We also present a numerical method to compute upper bounds for the minimal perturbations that move all eigenvalues of a given Hamiltonian matrix outside a vertical strip along the imaginary axis. KW - Hamiltonian matrix KW - Hamiltonian eigenvalue problem KW - perturbation theory KW - passive system KW - bounded-realness KW - purely imaginary eigenvalues KW - sign characteristic KW - Hamiltonian pseudospectra KW - structured mapping problem KW - distance to bounded-realness Y1 - 2011 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/692 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-6927 ER -