@article{bc4aff7e9ec540138600027319ce5350,
title = "Qualitative analysis of switched discrete-time descriptor systems",
abstract = "In this paper, we consider stability analysis and design for switched systems consisting of linear discrete-time descriptor subsystems. When all descriptor subsystems are stable, we show that if the descriptor matrix and all the subsystem matrices are commutative pairwise, then the switched system is stable under arbitrary switching. We also extend the result to the case where all subsystems have different descriptor matrices. Under the same commutation condition, we show that in the case where none of the descriptor subsystems is stable, if there is a stable combination of the unstable descriptor subsystems, then we establish a class of switching laws which stabilize the switched descriptor system. All the results are natural but important extensions to the existing results for switched systems composed of state space subsystems.",
keywords = "Arbitrary switching, Discrete-time descriptor systems, Stability analysis, Stabilization, Stable combination, Switched systems",
author = "Guisheng Zhai and Xuping Xu and Joe Imae and Tomoaki Kobayashi",
note = "Funding Information: Manuscript received April 28, 2007; revised April 26, 2008 and August 18, 2008; accepted December 29, 2008. Recommended by Editorial Board member Myotaeg Lim under the direction of Editor Jae Weon Choi. This research has been supported in part by the Japan Ministry of Education, Sciences and Culture under Grants-in-Aid for Scientific Research (B) 15760320 & 17760356. The authors would like to thank Mr. Ryuuen Kou with Osaka Prefecture University for valuable discussions, and thank the anonymous reviewers for suggestions and very careful check that helped to improve the paper. Guisheng Zhai, Joe Imae, and Tomoaki Kobayashi are with the Department of Mechanical Engineering, Osaka Prefecture University, Sakai, Osaka 599-8531, Japan (e-mails: {zhai, jimae, kobayasi}@me.osakafu-u.ac.jp).",
year = "2009",
month = aug,
doi = "10.1007/s12555-009-0402-6",
language = "English",
volume = "7",
pages = "512--519",
journal = "International Journal of Control, Automation and Systems",
issn = "1598-6446",
publisher = "Institute of Control, Robotics and Systems",
number = "4",
}