Volume 14 Number 5
October 2017
Article Contents
Xin-Quan Zhang, Xiao-Yin Li and Jun Zhao. Stability Analysis and Anti-windup Design of Switched Systems with Actuator Saturation. International Journal of Automation and Computing, vol. 14, no. 5, pp. 615-625, 2017. doi: 10.1007/s11633-015-0920-z
Cite as: Xin-Quan Zhang, Xiao-Yin Li and Jun Zhao. Stability Analysis and Anti-windup Design of Switched Systems with Actuator Saturation. International Journal of Automation and Computing, vol. 14, no. 5, pp. 615-625, 2017.

# Stability Analysis and Anti-windup Design of Switched Systems with Actuator Saturation

Author Biography:
• Xiao-Yin Li received the B. Sc. degree in applied mathematics from Shenyang Normal University, China in 2007. She received the M. Sc. degree in applied mathematics in 2012 at Liaoning Technical University of Fuxin, China. Since 2012, as a research intern, she has been with School of Foreign Languages, Liaoning Shihua University, China.
Her research interests include systems optimization, constrained systems and intelligent control.
E-mail:lxy1982_@163.com

Jun Zhao received the B. Sc. and M. Sc. degrees in mathematics in 1982 and 1984 respectively, both from Liaoning University, China. He received the Ph. D. in control theory and applications in 1991 at Northeastern University, China. From 1992 to 1993, he was a postdoctoral fellow at the same University. Since 1994, as a professor, he has been with College of Information Science and Engineering, Northeastern University, China. From 1998 to 1999, he was a senior visiting scholar at the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, USA. From November 2003 to May 2005, he was a research fellow at Department of Electronic Engineering, City University of Hong Kong. During 2007-2010, he was a fellow at School of Engineering, the Australian National University.
His research interests include switched systems, nonlinear systems and network synchronization.
E-mail:zhaojun@mail.neu.edu.cn

• Corresponding author: Xin-Quan Zhang received the B. Sc. degree in automation and M. Sc. degree in control theory & engineering from Liaoning Technical University, China in 2003 and 2007, respectively. He received the Ph. D. degree in control theory and control engineering in 2012 at the College of Information Science & Engineering, of the Northeastern University of Shenyang, China. Since 2012, as a lecturer, he has been with School of Information and Control Engineering, Liaoning Shihua University, China.
His research interests include switched systems, robust control and systems control under constraints.
E-mail:zxq_19800126@163.com(Corresponding author)
ORCID ID:0000-0003-0712-3671
• Accepted: 2014-11-18
• Published Online: 2017-10-07
Fund Project:

Scientific Research Fund of Education Department of Liaoning Province L2014159

• The stability analysis and anti-windup design problem is investigated for two linear switched systems with saturating actuators by using the single Lyapunov function approach. Our purpose is to design a switching law and the anti-windup compensation gains such that the maximizing estimation of the domain of attraction is obtained for the closed-loop system in the presence of saturation. Firstly, some sufficient conditions of asymptotic stability are obtained under given anti-windup compensation gains based on the single Lyapunov function method. Then, the anti-windup compensation gains as design variables are presented by solving a convex optimization problem with linear matrix inequality (LMI) constraints. Two numerical examples are given to show the effectiveness of the proposed method.
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[21] J. M. Gomes da Silva, S. Tarbouriech. Antiwindup design with guaranteed regions of stability:an LMI-based approach. IEEE Transactions on Automatic Control, vol. 50, no. 1, pp. 106-111, 2005.  doi: 10.1109/TAC.2004.841128 [22] X. Zhang, J. Zhao, G. M. Dimirovski. Robust state feedback stabilization of uncertain switched linear systems subject to actuator saturation. In Proceedings of the 2010 American Control Conference, IEEE, Marriott Waterfront Baltimore, USA, pp. 3289-3274, 2010. [23] L. Lu, Z. Lin, A switching anti-windup design using multiple Lyapunov functions. IEEE Transactions on Automatic Control, vol. 55, no. 1, pp. 142-148, 2010.  doi: 10.1109/TAC.2009.2033753 [24] A. Benzaouia, O. Akhrif, L. Saydy. Stabilization of switched systems subject to actuator saturation by output feedback. In Proceedings of the 45th IEEE Conference on Decision and Control, IEEE, San Diego, USA, pp. 777-782, 2006. [25] L. Lu, Z. Lin. 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## Stability Analysis and Anti-windup Design of Switched Systems with Actuator Saturation

• ###### Corresponding author:Xin-Quan Zhang received the B. Sc. degree in automation and M. Sc. degree in control theory & engineering from Liaoning Technical University, China in 2003 and 2007, respectively. He received the Ph. D. degree in control theory and control engineering in 2012 at the College of Information Science & Engineering, of the Northeastern University of Shenyang, China. Since 2012, as a lecturer, he has been with School of Information and Control Engineering, Liaoning Shihua University, China.     His research interests include switched systems, robust control and systems control under constraints.     E-mail:zxq_19800126@163.com(Corresponding author)    ORCID ID:0000-0003-0712-3671
Fund Project:

Scientific Research Fund of Education Department of Liaoning Province L2014159

Abstract: The stability analysis and anti-windup design problem is investigated for two linear switched systems with saturating actuators by using the single Lyapunov function approach. Our purpose is to design a switching law and the anti-windup compensation gains such that the maximizing estimation of the domain of attraction is obtained for the closed-loop system in the presence of saturation. Firstly, some sufficient conditions of asymptotic stability are obtained under given anti-windup compensation gains based on the single Lyapunov function method. Then, the anti-windup compensation gains as design variables are presented by solving a convex optimization problem with linear matrix inequality (LMI) constraints. Two numerical examples are given to show the effectiveness of the proposed method.

Xin-Quan Zhang, Xiao-Yin Li and Jun Zhao. Stability Analysis and Anti-windup Design of Switched Systems with Actuator Saturation. International Journal of Automation and Computing, vol. 14, no. 5, pp. 615-625, 2017. doi: 10.1007/s11633-015-0920-z
 Citation: Xin-Quan Zhang, Xiao-Yin Li and Jun Zhao. Stability Analysis and Anti-windup Design of Switched Systems with Actuator Saturation. International Journal of Automation and Computing, vol. 14, no. 5, pp. 615-625, 2017.
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