# Computing the stochastic $H^\infty$-norm

## TL;DR

This paper introduces a method to compute the stochastic $H^inity$-norm of linear systems using a Riccati-type matrix equation, providing a new approach without frequency domain or Hamiltonian conditions.

## Contribution

It develops a novel computational technique for the stochastic $H^inity$-norm based on a parametrized algebraic Riccati equation, extending deterministic methods.

## Key findings

- Provides a Riccati-based algorithm for stochastic $H^inity$-norm computation.
- Establishes theoretical characterization without frequency domain or Hamiltonian conditions.
- Enables practical computation for stochastic control systems.

## Abstract

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.