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Stability Analysis for State-constrained Switched Systems with All Subsystems Unstable

  • Control Theory and Applications
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Abstract

This paper mainly investigates the state constrained switched system with fully unstable subsystems. By limiting the state in a unit hypercube, a sufficient condition is derived to ensure the stability of such systems via a time-dependent strategy. The main idea is to use positive switching behavior to compensate state divergence caused by unstable states and setting a different ascend rate when state constraints occur or not. In order to make the conditions computable for a continuous-time switched systems with state constraints, the discretized Lyapunov Function method is applied, then a numerical example is given to show the practicability of the proposed method.

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Authors and Affiliations

  1. School of Automation Engineering, Northeast Electric Power University, Jilin, 132012, China

    Jian Li, Wen Li & Qingyu Su

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  1. Jian Li
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  2. Wen Li
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  3. Qingyu Su
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Correspondence to Qingyu Su.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Sung Jin Yoo under the direction of Editor Jessie (Ju H.) Park. This work is supported by the National Natural Science Foundation of China (61873057,61703384,61703091), Natural Science Foundation of Jilin Province (20180520211JH) and Jilin City Science and Technology Bureau (201831727, 201831731).

Jian Li received her B.Sc. and M.Sc. degrees in electrical automation and control theory and application from the Liaoning Technical University, China, in 2005 and 2008, respectively, and the Ph.D. degree in control theory and application from Northeast University, China in 2013. Currently, she is an Associate Professor in the School of Automation Engineering, Northeast Electric University, China. From July, 2015 to August, 2015, she was a visiting scholar at the Nonlinear Dynamics Group, Yeungnam University, South Korea. Her research interests include fault detection, robust control and micro-grid.

Wen Li received his B.Sc. degree in Automation in 2013 from North East Electric Power University, China. Now he is a master degree candidate at the School of Automation Engineering, Northeast Electric Power University, China. His research interests include switched systems and robust control.

Qingyu Su received his B.Sc. degree in electrical automation in 2005, and his M.Sc. degree in control theory and application in 2008, both from Liaoning Technical University, China. He completed his Ph.D. degree in control theory and application in 2013 at Northeastern University, China. Now he is an Associate Professor at the School of Automation Engineering, Northeast Electric University, China. From October 2015 to October 2016, he was a visiting scholar at the Intelligent Systems and Biomedical Robotics Group (ISR), University of Portsmouth, UK. He has published 13 articles on SCI Journals and 8 papers on international conferences. His research interests include switched systems, nonlinear control systems and power systems.

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Li, J., Li, W. & Su, Q. Stability Analysis for State-constrained Switched Systems with All Subsystems Unstable. Int. J. Control Autom. Syst. 17, 2482–2489 (2019). https://doi.org/10.1007/s12555-018-0569-9

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