Input-to-state stability analysis for a class of nonlinear switched descriptor systems

Abstract

This paper considers the problem of input-to-state stability for a class of nonlinear switched descriptor systems. According to the definition of input-to-state stability, sufficient conditions are derived to ensure that the system is input-to-state stable based on the dwell time approach and the Gronwall–Bellman inequality. Compared with existing methods, it is more convenient to design the controller for each subsystem, because it does not need to construct the input-to-state stable control Lyapunov function and design the specific structure of the control inputs. Finally, two numerical examples illustrate the feasibility and effectiveness of the proposed method.

Keywords:

• descriptor systems
• switched systems
• dwell time approach
• input-to-state stability

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61174032], [grant number 61104183]; the Program for New Century Excellent Talents in University [grant number NCET-10-0437]; the Fundamental Research Funds for the Central Colleges and Universities [grant number JUDCF11040].

Notes on contributors

Zairui Gao

Zairui Gao was born in Zaozhuang, Shandong Province, China, in 1982. He received his MS degree in operational research and cybernetics from Ludong University, China, in 2009, and his PhD degree in control theory and control engineering from Jiangnan University, China, in 2012. He is currently working in the School of Information and Control Engineering, Weifang University, China. His research interests include hybrid systems control and nonlinear switched systems.

Kun Yang

Kun Yang was born in Shandong Province, China. He received his MS degree in operational research and cybernetics from Ludong University, China, in 2010. He is currently a PhD student in Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, China. His current research interests include hybrid systems control, model predictive control and nonlinear switched systems.

Yanxia Shen

Yanxia Shen received her MS degree in control theory and engineering from Wuxi University of Light Industry, China, in 1999, and her PhD degree in power electronics and motor drives from China University of Mining and Technology, China, in 2004. In 2007–2008, she visited the power electronic laboratory in the University of California, Irvine, working with Prof. K.M. Smedley. Her research interests include power electronics, renewable energy technology and nonlinear control systems.

Zhicheng Ji

Zhicheng Ji received his BS degree in control engineering from the Southern Institute of Metallurgy, China, in 1978, and his PhD degree in power electronics and motor drives from China University of Mining and Technology, China, in 2003. In 2003, he visited the University of Toronto. Toronto, Canada. Since 2004 he has been working as a professor in control theory and control engineering at Jiangnan University, China. His research interests include renewable energy technology and nonlinear control systems.