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Robust Stabilization of Continuous-Time Nonlinear Switched Systems Without Stable Subsystems via Maximum Average Dwell Time

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Abstract

This paper investigates the robust stabilization problem for a class of polytopic uncertain continuous-time nonlinear switched systems without stable subsystems. In order to analyze the stability of switched systems without stable subsystems, we propose a novel switching Lyapunov function. This new switching Lyapunov function has the “switching-decreasing” property at switching instant. To obtain less conservative results, we propose the switching-decreasing parameter-dependent Lyapunov function (SDPDLF) to investigate the studied switched systems. By using the SDPDLF approach and maximum average dwell time technique, a sufficient condition is obtained to guarantee the studied switched systems to be asymptotically stable. It is shown that the average dwell time should be less than a upper bound. This is different from some previous work, where the average dwell time is larger than a lower bound. Finally, a numerical example and a practical example are provided to illustrate the effectiveness of our results.

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Acknowledgments

The work was supported in part by the National Natural Science Foundation of China (Grant Nos. 61374117, 61004048, 61174137, 61104038 and 61374086), the General Research Fund: CityU 101113 of RGC of Hong Kong SAR Government, the NSF of Jiang Su Province (Grant No. BK2010493), the grant from China Postdoctoral Science Foundation funded Project 2012M510135, the Program for Changjiang Scholars and Innovative Research Team in University, the Project from Science and Technology Department of Sichuan Province (Grant No. 2014GZ0156) and the 973 Project 2011CB707000.

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  1. School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, People’s Republic of China

    Qunxian Zheng & Hongbin Zhang

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  1. Qunxian Zheng
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  2. Hongbin Zhang
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Correspondence to Qunxian Zheng.

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Zheng, Q., Zhang, H. Robust Stabilization of Continuous-Time Nonlinear Switched Systems Without Stable Subsystems via Maximum Average Dwell Time. Circuits Syst Signal Process 36, 1654–1670 (2017). https://doi.org/10.1007/s00034-016-0376-6

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