Balanced truncation of k-positive systems

作     者：Grussler, Christian Damm, Tobias Sepulchre, Rodolphe 

作者机构：The Department of Electrical Engineering and Computer Sciences UC Berkeley BerkeleyCA94720 United States The Department of Mathematics at TU Kaiserslautern Fraunhofer ITWM Gottlieb-Daimler-Straße 48 Kaiserslautern67663 Germany The Control Group The Department of Engineering University of Cambridge Trumpington Street CambridgeCB2 1PZ United Kingdom 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2020年

核心收录：

主　　题：Matrix algebra 

摘      要：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 (∞-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 *** Codes 47A58, 93A15, 93A30 Copyright © 2020, The Authors. All rights reserved.