Dissipative control for a class of nonlinear descriptor systems

Abstract

This paper is concerned with the dissipative control problem for a class of nonlinear descriptor systems. Based on Lyapunov stability theory, sufficient conditions are derived, which guarantee that the underlying systems are strictly dissipative. Then, the design method for a state feedback controller is provided. All the conditions can be expressed via linear matrix inequalities. Finally, a numerical example is presented to demonstrate the validity of the proposed methods.

Keywords:

• descriptor systems
• dissipative control
• state feedback controller
• linear matrix inequalities (LMIs)
• bilinear matrix inequality

Additional information

Funding

This work was supported by the Natural Science Foundation of China [grant number 60974004], [grant number 61273008], [grant number 61203001]; the Nature Science of Foundation of Liaoning Province [grant number 201202063].

Notes on contributors

Juan Zhou

Juan Zhou received her MS degree from Jilin University in 2006. She is currently a lecturer in the Northeastern University. Her research interests are in the areas of descriptor systems.

Qingling Zhang

Qingling Zhang is a professor at the Northeastern University, Shenyang, China. He received his BS and MS degrees from the Mathematics Department and his PhD degree from the Automatic Control Department of the Northeastern University, in 1982, 1986, and 1995, respectively. His main research interests are descriptor systems, biological control, network control, and dissipative control. He has published eight books and more than 260 papers about control theory and applications. Professor Zhang received 14 prizes from central and local governments for his research. He has also received the Golden Scholarship from Australia in 2000.

Jinghao Li

Bo Men received her PhD degree from the Institute of System Sciences, Northeastern University, in 2013. She is currently a lecturer in Shenyang Normal University. Her research interests are in the areas of switched systems and singular systems.

Bo Men

Jinghao Li received his BSc degree in mathematics from the Northeastern University, Shenyang, China, in 2011. He is now pursuing his MSc degree in systems theory from the Northeastern University, China. His current research interests focus on descriptor Markovian jump systems.

Junchao Ren

Junchao Ren received his BSc degree in applied mathematics from the Northeastern University, Shenyang, China, in 2000, his MSc degree in control theory and control engineering from Guangdong University of Technology, Guangzhou, in 2003, and his PhD degree in control theory and control engineering from the Northeastern University, Shenyang, China, in 2011. Dr Ren is currently an associate professor with the Institute of Systems Science, Northeastern University, Shenyang, China. His research interests include robust control and singular systems.