{"ID":5551846,"CreatedAt":"2026-07-02T01:54:51.863792489Z","UpdatedAt":"2026-07-04T07:28:02.592842364Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.00552","arxiv_id":"2607.00552","title":"L2-L2-gain bounds for quadratic output systems","abstract":"We derive an explicit bound for the L2-L2-gain of linear time-invariant systems whose output is a quadratic function of the state and the input. Such systems appear naturally in many areas, for example for port-Hamiltonian systems, optimal-control, and stochastic problems. In case the output is purely quadratic in the state, the bound equals the L2-norm of the bivariate transfer function evaluated along the anti-diagonal $\\{(s,\\,-s)\\mid s\\in i\\mathbb R\\}$ of the $i \\mathbb R\\times i \\mathbb R$ frequency domain. Further, we show how the bound can be computed by solving linear matrix equations. This result provides a practical tool for assessing and reducing quadratic-output models.","short_abstract":"We derive an explicit bound for the L2-L2-gain of linear time-invariant systems whose output is a quadratic function of the state and the input. Such systems appear naturally in many areas, for example for port-Hamiltonian systems, optimal-control, and stochastic problems. In case the output is purely quadratic in the...","url_abs":"https://arxiv.org/abs/2607.00552","url_pdf":"https://arxiv.org/pdf/2607.00552v1","authors":"[\"Birgit Hillebrecht\"]","published":"2026-07-01T07:43:25Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.DS\"]","methods":"[]","has_code":false}