×

Perturbation theory for Hamiltonian matrices and the distance to bounded-realness. (English) Zbl 1227.93081

Summary: 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.

MSC:

93C73 Perturbations in control/observation systems
93B36 \(H^\infty\)-control
93B40 Computational methods in systems theory (MSC2010)
49N35 Optimal feedback synthesis
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
93B52 Feedback control
93C05 Linear systems in control theory

Software:

Eigtool; Seigtool
PDFBibTeX XMLCite
Full Text: DOI