Stability analysis for delta operator systems subject to state saturation

ABSTRACT

In this paper, we investigate the problem of stability analysis for linear delta operator systems subject to state saturation. Both full state saturation and partial state saturation are investigated for the delta operator systems. Two equivalent necessary and sufficient conditions are identified such that the system with full state saturation is globally asymptotically stable. Based on the sufficient conditions, an iterative algorithm is proposed for testing global asymptotic stability of the system with full state saturation. A new globally asymptotically stable condition is also proposed for the partial state saturation system. Two numerical examples on a ball and beam model are given to show the effectiveness of the proposed method.

Keywords:

• State saturation
• delta operator system
• stability analysis
• partial state saturation

Acknowledgements

The authors would like to thank the anonymous reviewers for their detailed comments which helped to improve the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

National Basic Research Program of China (973 Program) [grant number 2012CB720000)]; PhD Programs Foundation of Ministry of Education of China [grant number 20111101110012]; National Natural Science Foundation of China [grant numbers 61573301, 61225015 and 61403330]; Postdoctoral Science Foundation of China [grant number 2014M551052]; Hebei Provincial Natural Science Fund [grand number F2015203163]; Natural Science Foundation of Hebei Education Department [grant number QN2014068].

Notes on contributors

Hongjiu Yang

Hongjiu Yang was born in Hebei Province, China, in 1981. He received his BS degree in mathematics and applied mathematics and MS degree in applied mathematics from Hebei University of Science and Technology, Shijiazhuang, China, in 2005 and 2008, respectively. He received his PhD degree in control science and engineering in Beijing Institute of Technology, Beijing, China. He is currently an associate professor with the Department of Automation, Institute of Electrical Engineering, Yanshan University, China. His main research interests include robust control/filter theory, delta operator systems, networked control systems and active disturbance rejection control.

Qing Geng

Qing Geng was born in Hebei Province, China, in 1989. She received her BS degree in mathematics and applied mathematics from Hebei University of Science and Technology, Shijiazhuang, China, in 2014. She is currently working toward the MS degree at the Department of Electrical Engineering, Yanshan University. Her main research interests actuator saturation, delta operator systems and networked control systems.

Yuanqing Xia

Yuanqing Xia received his MS degree in Fundamental Mathematics from Anhui University, China, in 1998 and PhD degree in Control Theory and Control Engineering from Beijing University of Aeronautics and Astronautics, China, in 2001. He is currently a Professor with the Department of Automatic Control, Beijing Institute of Technology, Beijing. His research interests are in the fields of networked control systems, robust control, active disturbance rejection control and biomedical signal processing.

Li Li

Li Li received her BS degree in Mathematics and Applied Mathematics from Hebei Normal University, China, in 2006, MS degree in Applied Mathematics from Hebei University of Science and Technology, China, in 2009 and PhD degree in Control Science and Engineering in Beijing Institute of Technology, Beijing, China, in 2013. She is currently a teacher with the College of Electrical Engineering, Yanshan University, China. Her research interests are in the fields of nonlinear filtering, robust control, fuzzy system, networked control systems.