Van Loan, Charles2007-04-232007-04-231984-10http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR84-649https://hdl.handle.net/1813/6488In this paper we explore how close a given stable matrix A is to being unstable. As a measure of "how stable" a stable matrix is, the spectral abscissa is shown to be flawed. A better measure of stability is the Frobenius norm of the smallest perturbation that shifts one of A's eigenvalues to the imaginary axis. This leads to a singular value minimization problem that can be approximately solved by heuristic means. However, the minimum destabilizing perturbation may be complex even when A is real. This suggests that in the real case we look for the smallest real perturbation that shifts one of the eigenvalues to the imaginary axis. Unfortunately, a difficult constrained minimization problem ensues and no practical estimation technique could be devised.1247022 bytes330014 bytesapplication/pdfapplication/postscripten-UScomputer sciencetechnical reporttechnical report