Event-triggered Control of Positive Switched Systems with Actuator Saturation and Time-delay

Abstract

This paper investigates the event-triggered control of positive switched systems with randomly occurring actuator saturation and time-delay, where the actuator saturation and time-delay obey different Bernoulli distributions. First, an event-triggering condition is constructed based on a 1-norm inequality. Under the presented event-triggering scheme, an interval estimation method is utilized to deal with the error term of the systems. Using a co-positive Lyapunov functional, the event-triggered controller and the cone attraction domain gain matrices are designed via matrix decomposition techniques. The positivity and stability of the resulting closed-loop systems are reached by guaranteeing the positivity of the lower bound of the systems and the stability of the upper bound of the systems, respectively. The proposed approach is developed for interval and polytopic uncertain systems, respectively. Finally, two examples are provided to illustrate the effectiveness of the theoretical findings.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Nos. 62073111 and 61751304), Fundamental Research Funds for the Provincial Universities of Zhejiang (No. GK209907299001-007), Natural Science Foundation of Zhejiang Province, China (Nos. LY20F030008 and LY20F030011), and Foundation of Zhejiang Provincial Department of Education (No. Y201942017).

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Correspondence to Jun-Feng Zhang.

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Jun-Feng Zhang received the Ph. D. degree in Shanghai Jiao Tong University, China in 2014. From December 2014, he worked in School of Automation, Hangzhou Dianzi University, China. From August 2019 to August 2020, he visited Inria, University of Lille, France. He is a member of IEEE and CAA. He was the co-chair of Program Committee in the 6th International Conference on Positive Systems. He has published more than 50 journal and conference papers in the field of positive systems.

His research interests include positive systems, switched systems, and model predictive control.

Lai-You Liu received the B. Sc. degree in Zhengzhou University of Aeronautics, China in 2017. He is a master student in Hangzhou Dianzi University, China.

His research interests include positive systems and hybrid systems. E-mail: laiyouliu@126.com

Shi-Zhou Fu received the B. Sc. degree in Hangzhou Dianzi University, China in 2010. He received the Ph. D. degree in Hong Kong University, China in 2015. He was appointed as a lecturer at Hangzhou Dianzi University, China in 2016.

His research interests include fuzzy control, quantum control and robust control. E-mail: fushizhou@hdu.edu.cn

Shuo Li received the Ph. D. degree in control science and engineering from Nanjing University of Science and Technology, China in 2017. She was appointed as a lecturer at Hangzhou Dianzi University, China in 2017.

Her research interests include positive systems, switched systems, and fuzzy systems.

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Zhang, JF., Liu, LY., Fu, SZ. et al. Event-triggered Control of Positive Switched Systems with Actuator Saturation and Time-delay. Int. J. Autom. Comput. 18, 141–154 (2021). https://doi.org/10.1007/s11633-020-1245-0

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Keywords

  • Positive switched systems
  • event-triggered control
  • randomly occurring actuator saturation
  • linear programming
  • time-delay