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arXiv · 2006.13333

Balanced truncation of $k$-positive systems

Christian Grussler·Tobias Damm·Rodolphe Sepulchre
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Abstract

This paper considers balanced truncation of discrete-time Hankel $k$-positive systems, characterized by Hankel matrices whose minors up to order $k$ are nonnegative. Our main result shows that if the truncated system has order $k$ or less, then it is Hankel totally positive ($\infty$-positive), meaning that it is a sum of first order lags. This result can be understood as a bridge between two known results: the property that the first-order truncation of a positive system is positive ($k=1$), and the property that balanced truncation preserves state-space symmetry. It provides a broad class of systems where balanced truncation is guaranteed to result in a minimal internally positive system.

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Christian Grussler, Tobias Damm, Rodolphe Sepulchre. 2020-06-23. Balanced truncation of $k$-positive systems. https://doi.org/10.1109/tac.2021.3075319

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