A Newton-based method for the calculation of the distance to instability (Q716432)

The authors introduce a new fast algorithm for computing the distance of a stable matrix, with all its eigenvalues in the left half-plane, to the set of unstable matrices. The first component of the algorithm is a local method based on Newtons's method, and though very quick, is not guaranteed to find a globally optimal solution. For that reason, a checking step is added to provide a global method. Numerical results show that this algorithm is competitive with and, in almost all cases, outperforms earlier algorithms. Five numerical examples are considered.