Computing the stochastic H∞ - norm by a netwon iteration

The stochastic H∞-norm is defined as the L2-induced norm of the input-output operator of a stochastic linear system. Like the deterministic H∞-norm it is characterized by a version of the bounded real lemma, but without a frequency domain description or a Hamiltonian condition. Therefore, we base its computation on a parametrized algebraic Riccati-type matrix equation and a Newton iteration. For large dimensions, our algorithm outperforms LMI-methods