Data-based controllability analysis of discrete-time linear time-delay systems

Abstract

In this paper, a data-based method is used to analyse the controllability of discrete-time linear time-delay systems. By this method, one can directly construct a controllability matrix using the measured state data without identifying system parameters. Hence, one can save time in practice and avoid corresponding identification errors. Moreover, its calculation precision is higher than some other traditional approaches, which need to identify unknown parameters. Our methods are feasible to the study of characteristics of deterministic systems. A numerical example is given to show the advantage of our results.

Keywords:

• controllability
• time-delay
• linear discrete-time system
• data-based method

Acknowledgements

This work was partially supported by the NNSF of China (Grant nos. 61175119, 11101373, 11271333 and 61074011), the NSF of Jiangsu Province of China (Grant no. BK2010408), Huo Ying-Dong Education Foundation (Grant No. 132037) and Zhejiang Innovation Project, China (Grant no. T200905).

Additional information

Notes on contributors

Yang Liu

Yang Liu received the B.S. degree in Mathematics from Zhejiang Normal University, Zhejiang, China, in 2003, and the Ph.D. degree from Tongji University, Shanghai, in 2008. He is currently an Associate Professor in the Department of Mathematics, Zhejiang Normal University. His research interests include complex analysis, Clifford analysis, switched systems, delayed systems and nonlinear control. He has published over 20 papers in refereed international journals. He is the recipient of the Shanghai Outstanding Ph.D’s Thesis Award in 2011.

Hong-Wei Chen

Hong-Wei Chen received the B.S. degree in Mathematics from Qiongzhou University, Sanya, China, in 2011. Since 2011 he has been pursuing his M.S. degree in Physics and Information Engineering, Zhejiang Normal University, Jinhua, China. His research interests include logical dynamic systems, systems biology, etc.

Jian-Quan Lu

Jian-Quan Lu received the B.S. degree in Mathematics from Zhejiang Normal University, Zhejiang, China, in 2003, the M.S. degree in Mathematics from Southeast University, Nanjing, China, in 2006, and the Ph.D. degree from City University of Hong Kong, Hong Kong, in 2009. He is currently an Associate Professor in the Department of Mathematics, Southeast University, Nanjing, China. His current research interests include collective behavior in complex dynamical networks, multi-agent systems and nonlinear systems and control.

He has published over 30 papers in refereed international journals. Dr Lu is an Associate Editor of Neural Processing Letters (Springer) and Neural Computing and Applications (Springer), and a Guest Editor of Mathematics and Computers in Simulation (Elsevier). He is the recipient of the Jiangsu Provincial Outstanding Master’s Thesis Award in 2007, TOP 100 Most Cited Chinese Papers Published in International Journals in 2007, an Alexander von Humboldt Fellowship in 2010, Program for New Century Excellent Talents in University by The Ministry of Education, China, in 2010, and The First Award of Jiangsu Provincial Progress in Science and Technology in 2010 as the Second Project Member.