A Cone-preserving Solution to a Nonsymmetric Riccati Equation

2024/11/18 by Emil Vladu, Anders Rantzer, Vladu, Emil +1
Mathematics · #FOS: Mathematics #Fractional Differential Equations Solutions #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2411.14470

openalex publication_date 2024/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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