Dynamic Event-Triggered Sliding Mode Control of Markov Jump Delayed System with Partially Known Transition Probabilities

Jie Lu, Yang Jia (), Xiang Cai, Jinnan Luo and Jiachen Li
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Jie Lu: Shanghai Polytechnic University, Shanghai 201209, China
Yang Jia: College of Electrical Engineering, Southwest Minzu University, Chengdu 610041, China
Xiang Cai: Shanghai Polytechnic University, Shanghai 201209, China
Jinnan Luo: College of Electrical Engineering, Southwest Minzu University, Chengdu 610041, China
Jiachen Li: College of Electrical Engineering, Southwest Minzu University, Chengdu 610041, China

Mathematics, 2025, vol. 13, issue 5, 1-23

Abstract: This paper investigates the dynamic event-triggered (ET) sliding mode control (SMC) of Markov jump delayed systems (MJDSs) with partially known transition probabilities. Firstly, a dynamic ET scheme is introduced for the Markov SMC system, and the effect of time delays is considered. In addition, the Razumikhin condition is used to deal with the time delay. Moreover, in the case of a Markov jump system with partially known transition probabilities, using the vertex method, weak infinitesimal generator, and Dynkin’s formula, the finite-time boundness (FTB) problem of a class of ET SMC systems with stochastic delay is studied. Finally, a numerical example is given to illustrate the viability of our results.

Keywords: Markov jump linear systems (MJLSs); unknown transition rates; sliding mode control; event-triggered (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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