Non-fragile reliable control for positive Markovian jump systems based on event-triggered mechanism

Abstract

This paper is concerned with the non-fragile reliable control of positive Markovian jump systems with actuator saturation based on event-triggered mechanism. First, an event-triggering condition is given in the form of 1-norm. Using a stochastic co-positive Lyapunov function, a design approach is proposed for the non-fragile controller gain and the corresponding auxiliary feedback gain. Under the designed controller, the closed-loop system is positive and stochastically stable even if actuator faults occur. A cone is constructed as the invariant set of the systems. All conditions are solvable in terms of linear programming. Finally, two examples are provided to verify the effectiveness of the obtained results.

Keywords:

• Non-fragile reliable control
• event-triggered mechanism
• positive Markovian systems
• linear programming

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Nature Science Foundation of China [Nos. 62073111 and 61751304], the Fundamental Research Funds for the Provincial Universities of Zhejiang [No. GK209907299001-007], the Natural Science Foundation of Zhejiang Province, China [Nos. LY20F030008 and LY20F030011], and the Foundation of Zhejiang Provincial Department of Education No. Y202044335].

Notes on contributors

Yinggang Feng

Yinggang Feng received his B.S. degree in North China University of Water Resources and Electric Power. He began to pursue his Master's degree in Hangzhou Dianzi University in September 2019. His research interests refer to positive systems and Markovian systems.

Junfeng Zhang

Junfeng Zhang received his Ph.D. degree in Shanghai Jiao Tong University in 2014. From December 2014, he worked in the School of Automation, Hangzhou Dianzi University. From August 2019 to August 2020, he visited Inria, University of Lille, France. 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 and one book in the field of positive systems. His research interests include positive systems, switched systems, and model predictive control.

Shuo Li

Shuo Li received her Ph.D. degree in Nanjing University of Science and Technology in 2017. She was appointed as lecturer at Hangzhou Dianzi University in 2017. Her research interests include positive systems, switched systems, and fuzzy systems.

Shizhou Fu

Shizhou Fu received his B.S. degree in Hangzhou Dianzi University in 2010. He received his Ph.D. degree in Hong Kong University in 2015. He was appointed as lecturer at Hangzhou Dianzi University in 2016. His research interests include fuzzy control, quantum control, and robust control.