Event-triggered network-based ℓ₁-gain filtering for positive linear systems

ABSTRACT

The ℓ₁-gain filtering problem of positive linear discrete-time systems based on networked communication is investigated in this paper. A filter system model in which the sampled signals are transmitted through the unreliable communication channels is constructed for a positive system. An event-triggered scheme in a linear form, which is different from the prior literatures, is designed to determine whether the signal packet should be transmitted to the filter or not. Network-induced delays are considered while handling the packet transmission. By using the linear Lyapunov function method, a sufficient condition to ensure the existence of the network-based positive filter satisfying ℓ₁-gain performance is proposed. The desired filter design method for the positive system is presented by using a linear programming approach. A numerical example with practical considerations is given to verify the proposed theoretical results.

KEYWORDS:

• Positive system
• network-based filter
• event-triggered scheme
• ℓ₁-gain filter
• time-delay

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported in part by the National Natural Science Foundation of China [grant numbers 61473152, 61473151 and 61304136]; the Program for New Century Excellent Talents in University [grant number NCET-13-0859]; the Natural Science Fund for Distinguished Young Scholars of Jiangsu Province [grant number BK20150034]; Qing Lan Project.

Notes on contributors

Shunyuan Xiao

Shunyuan Xiao received his B.Eng. degree in Electrical Engineering and Automation from Nanjing University of Science and Technology, Nanjing, China, in 2014. He is currently a Ph.D. candidate of control theory and control engineering in School of Automation, Nanjing University of Science and Technology. His research interests include networked control systems and positive systems.

Yijun Zhang

Yijun Zhang received his B.S. degree in applied mathematics from Nanjing Meteorological Institute, China, in 2002, M.S. degree in Operational Research and Cybernetics from Nanjing Normal University, China, in 2005, and Ph.D. in control theory and control engineering from Donghua University, China, in 2008. From 2008 to 2011, he was a postdoctoral fellow in Nanjing University of Science and Technology, China. He was a visiting scholar in the Center for Intelligent and Networked Systems, Central Queensland University, Australia, from December 2010 to June 2011, and a visiting scholar in the Engineering Department, University of Leicester, UK, from January 2012 to January 2013. Currently, he is an Associate Professor at Nanjing University of Science and Technology, China. His research interests include complex networks, networked control systems, and nonlinear system control.

Qiyi Xu

Qiyi Xu was born in Shandong Province, China, in 1981. He received his M.S. degree in Control Theory and Control Engineering from Qufu Normal University, Qufu, China, in 2007. Now he is a Ph.D. candidate of Control Theory and Control Engineering in the School of Automation, Nanjing University of Science and Technology, Nanjing, China. His current research interests include networked control systems and singular systems.

Baoyong Zhang

Baoyong Zhang received his B.Sc. degree and M.Sc. degree from Qufu Normal University, Qufu, China, in 2003 and 2006, respectively, and Ph.D. degree from Nanjing University of Science and Technology (NJUST), Nanjing, China, in 2011. From March 2008 to June 2008, he was a Research Associate in the Department of Mechanical Engineering, the University of Hong Kong, Hong Kong. From November 2008 to July 2009, he was a Visiting Fellow at the School of Computing and Mathematics, the University of Western Sydney, Penrith NSW, Australia. From December 2011 to December 2012, he was a Postdoctoral Fellow in the Department of Mechanical Engineering, the University of Hong Kong, Hong Kong. He joined the School of Automation at NJUST as Lecturer in November 2010 and was selected as Young Professor of NJUST in August 2014. His research interests include robust control and filtering, time-delay systems, stochastic systems, switched systems, nonlinear systems, LPV systems and complex networks.