A Cone-preserving Solution to a Nonsymmetric Riccati Equation

Emil Vladu; Anders Rantzer

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arXiv · 2411.14470

A Cone-preserving Solution to a Nonsymmetric Riccati Equation

Emil Vladu·Anders Rantzer

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Abstract

In this paper, we provide the following simple equivalent condition for a nonsymmetric Algebraic Riccati Equation to admit a stabilizing cone-preserving solution: an associated coefficient matrix must be stable. The result holds under the assumption that said matrix be cross-positive on a proper cone, and it both extends and completes a corresponding sufficient condition for nonnegative matrices in the literature. Further, key to showing the above is the following result which we also provide: in order for a monotonically increasing sequence of cone-preserving matrices to converge, it is sufficient to be bounded above in a single vectorial direction.

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BibTeX RIS

Emil Vladu, Anders Rantzer. 2024-11-18. A Cone-preserving Solution to a Nonsymmetric Riccati Equation. https://arxiv.org/abs/2411.14470

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