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arXiv · 2509.09256

Partial Eigenvalue Assignment for Nonlinear Systems

Shang Wang·Xiaodong Cheng·Yu Kawano·Peter van Heijster
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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.

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Shang Wang, Xiaodong Cheng, Yu Kawano, Peter van Heijster. 2025-09-11. Partial Eigenvalue Assignment for Nonlinear Systems. https://arxiv.org/abs/2509.09256

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