Measures for Robust Stability and Controllability
Eigenvalue optimization characterizations and their numerical solution
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This work investigates some of the quantities indicating the degree of robustness of a dynamical system; all intrinsically have ties with the sensitivity of the eigenvalues. The emphasis is put on the computation of these quantities rather than further analysis of their effectiveness in indicating the robustness. The algorithms devised benefit from equivalent singular-value or eigenvalue optimization characterizations. The difficulty that we attempt to overcome is the nonconvex nature of these optimization problems. Surprisingly the global extrema of these nonconvex problems are located reliab...
This work investigates some of the quantities indicating the degree of robustness of a dynamical system; all intrinsically have ties with the sensitivity of the eigenvalues. The emphasis is put on the computation of these quantities rather than further analysis of their effectiveness in indicating the robustness. The algorithms devised benefit from equivalent singular-value or eigenvalue optimization characterizations. The difficulty that we attempt to overcome is the nonconvex nature of these optimization problems. Surprisingly the global extrema of these nonconvex problems are located reliably and with a decent amount of work (usually by means of a fast converging algorithm with a cubic cost at each iteration) by the help of structured eigenvalue solvers and iterative eigenvalue solvers.
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