Georgia Institute of Technology College of Sciences

The distance of a nxn stable matrix to the set of unstable matrices, the so-called distance to instability, is a well-known measure of linear dynamical system stability. Existing techniques compute this quantity accurately but the cost is of the order of multiple SVDs of order n, which makes the method suitable to middle size problems. A new approach is presented, based on Newton's iteration applied to pseudospectral abscissa, whose implementation is obtained by discretization on differential equation for low-rank matrices, particularly suited for large sparse matrices.