J Shanghai Jiaotong Univ Sci ›› 2022, Vol. 27 ›› Issue (5): 723-736.doi: 10.1007/s12204-021-2335-z

• Automation System & Theory • Previous Articles     Next Articles

Event-Triggered Control of Positive Semi-Markovian Jump Systems Without/with Input Saturation

ZHANG Suhuan (张素焕), ZHANG Junfeng∗ (张俊锋), LI Shuo (李烁), YU Shanen (余善恩)   

  1. (School of Automation, Hangzhou Dianzi University, Hangzhou 310018, China)
  • Received:2019-10-17 Online:2022-09-28 Published:2022-09-03

Abstract: This paper is concerned with the event-triggered control of positive semi-Markovian jump systems without/with input saturation. The considered systems are subject to a stochastic semi-Markovian process whose sojourn time is dependent on a non-exponential distribution. First, an event-triggering condition is introduced in a linear form for the systems. A class of event-triggered feedback controllers is proposed using matrix decomposition technique. By using a stochastic co-positive Lyapunov function, the systems’ positivity and stability are guaranteed. Then, the obtained results are developed for the systems with input saturation. A cone set is chosen as the attraction domain and the corresponding attraction domain gain matrix is designed in terms of standard linear programming approach. Finally, two numerical examples are provided to verify the validity and effectiveness of the presented theoretical findings.

Key words: event-triggered control, positive semi-Markovian jump systems, input saturation, matrix decomposition, linear programming

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