Computing the stochastic $H^\infty$-norm
It provides a novel computational approach for a key norm in stochastic systems theory, relevant for control and robustness analysis.
The paper defines the stochastic H∞-norm for stochastic linear systems and proposes a computational method based on a parametrized algebraic Riccati-type matrix equation, addressing the lack of frequency-domain or Hamiltonian characterizations.
The stochastic $H^\infty$-norm is defined as the $L^2$-induced norm of the input-output operator of a stochastic linear system. Like the deterministic $H^\infty$-norm it is characterised 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 parametrised algebraic Riccati-type matrix equation.