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.
Cite
@article{arxiv.2509.09256,
title = {Partial Eigenvalue Assignment for Nonlinear Systems},
author = {Shang Wang and Xiaodong Cheng and Yu Kawano and Peter van Heijster},
journal= {arXiv preprint arXiv:2509.09256},
year = {2025}
}