A new approach for calculating the real stability radius (Q398622)

This paper presents a fast method for the calculation of the so-called real stability radius of the given dynamical system. This method exploits a relationship between singular values of the transfer function and imaginary eigenvalues of the three-parameter Hamiltonian matrix. The critical point is found using the implicit determinant method. The presented approach requires only to solve a linear system in each Newton step (instead of solving the singular value and the Hamiltonian eigenvalue problems). On the other hand, the convergence is only local, thus this approach highly depends on a good initial guess. Some strategies for the inital guess are discussed. The authors illustrate their new approach on numerical examples.