Robust stability and a criss-cross algorithm for pseudospectra |
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| Authors: | Burke, J. V. Lewis, A. S. Overton, M. L. |
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| Affiliation: | 1 Department of Mathematics, University of Washington, Seattle, WA 98195, USA 2 Department of Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada 3 Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA |
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| Abstract: | A dynamical system  = Ax is robustly stablewhen all eigenvalues of complex matrices within a given distanceof the square matrix A lie in the left half-plane. The pseudospectralabscissa, which is the largest real part of such an eigenvalue,measures the robust stability of A. We present an algorithmfor computing the pseudospectral abscissa, prove global andlocal quadratic convergence, and discuss numerical implementation.As with analogous methods for calculating H norms, our algorithmdepends on computing the eigenvalues of associated Hamiltonianmatrices. |
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| Keywords: | pseudospectrum eigenvalue optimization robust control stability spectral abscissa H![]("</a) /math/infin.gif" ALT=" {infty}" BORDER=" 0" > norm robust optimization Hamiltonian matrix |
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