Balanced truncation of k-positive systems

Grussler, C and Damm, T and Sepulchre, R (2021) Balanced truncation of k-positive systems. IEEE Transactions on Automatic Control. ISSN 0018-9286

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Abstract

This paper considers balanced truncation of discrete-time Hankel <formula><tex>$k$</tex></formula>-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 <formula><tex>$k$</tex></formula> or less, then it is Hankel totally positive (<formula><tex>$\infty$</tex></formula>-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 (<formula><tex>$k=1$</tex></formula>), 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.

Item Type: Article UNSPECIFIED Div F > Control Cron Job 07 May 2021 22:14 02 Sep 2021 05:30 10.1109/TAC.2021.3075319