Dynamic event‐triggered control for Markovian jump linear systems with time‐varying delay

• Published in: International journal of robust and nonlinear control Vol. 32; no. 4; pp. 2359 - 2379
• Main Authors: Zhao, Hui, Li, Weidong, Li, Zhicheng, Ren, Yu
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 10.03.2022
• Subjects: Control systems design; Delay; dynamic event‐triggered control; Event triggered control; input–output approach; Linear systems; Markovian jump linear systems; stochastic stability analysis; time‐varying delay; Transmission efficiency
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.5954

In this article, the problem of dynamic event‐triggered control (ETC) for Markovian jump linear systems (MJLSs) with time‐varying delay is investigated. First, the original system is transformed into an interconnection system with input–output form. Then, the dynamic ETC is proposed to reduce the transmission frequency. Meanwhile, the conditions of stochastic stability are proposed by constructing a novel stochastic Lyapunov–Krasovskii functional and using the scaled stochastic small‐gain theorem. Further, the controller design method is presented to stabilize the closed‐loop MJLSs with time‐varying delay. The merit of this article lies in that the conservatism for stability results is reduced and the transmission efficiency is improved by reducing the event‐triggered times, which is made possible by designing dynamic ETC. Finally, two numerical examples are provided to demonstrate the advantages and effectiveness of the proposed methods.