{"ID":2872118,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.09256","arxiv_id":"2509.09256","title":"Partial Eigenvalue Assignment for Nonlinear Systems","abstract":"In this paper, we study control design methods for assigning a subset of nonlinear right or left eigenvalues to a specified set of scalar-valued functions via nonlinear Sylvester equations. This framework can be viewed as a generalization of partial linear eigenvalue assignment (also referred to as partial pole placement) for linear systems. First, we propose a method for partial nonlinear right eigenvalue assignment via state feedback using a nonlinear Sylvester equation and a condition for preserving an open-loop nonlinear right eigenvalue. This method can be applied to partial stabilization of nonlinear systems. Then, as the dual problem, we present a method for partial nonlinear left eigenvalue assignment via the dual nonlinear Sylvester equation and a condition for preserving an open-loop nonlinear left eigenvalue, which can be applied to partial observer design for nonlinear system.","short_abstract":"In this paper, we study control design methods for assigning a subset of nonlinear right or left eigenvalues to a specified set of scalar-valued functions via nonlinear Sylvester equations. This framework can be viewed as a generalization of partial linear eigenvalue assignment (also referred to as partial pole placeme...","url_abs":"https://arxiv.org/abs/2509.09256","url_pdf":"https://arxiv.org/pdf/2509.09256v1","authors":"[\"Shang Wang\",\"Xiaodong Cheng\",\"Yu Kawano\",\"Peter van Heijster\"]","published":"2025-09-11T08:41:03Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}