Event-Triggered Control for Markov Jump Systems Subject to Mismatched Modes and Strict Dissipativity

• Published in: IEEE transactions on cybernetics Vol. 53; no. 3; pp. 1537 - 1546
• Main Authors: Tao, Jie, Xiao, Zehui, Chen, Jiawei, Lin, Ming, Lu, Renquan, Shi, Peng, Wang, Xiaofeng
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.03.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asynchronous dissipativity control; Closed loop systems; Closed loops; Control systems design; Controllers; Discrete time systems; Dissipation; Event triggered control; event-triggered mechanism; Feedback control; Hidden Markov models; Liapunov functions; Linear matrix inequalities; Markov chains; Markov jump systems; Markov processes; randomly occurring uncertainties; Symmetric matrices; Task analysis; Uncertainty
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2021.3105179

In order to save network resources of discrete-time Markov jump systems, an event-triggered control framework is employed in this article. The threshold parameter in the event-triggered mechanism is designed as a diagonal matrix in which all elements can be adjusted according to system performance requirements. The hidden Markov model is introduced to characterize the asynchronization between the controller and controlled system. The effect of randomly occurring gain fluctuations is taken into account during the controller design. For the purpose of guaranteeing that the closed-loop system is stochastically stable and satisfies the strictly <inline-formula> <tex-math notation="LaTeX">(\mathcal {D}_{1},\mathcal {D}_{2},\mathcal {D}_{3})-\gamma - </tex-math></inline-formula>dissipative performance, sufficient conditions are constructed by employing the Lyapunov function and stochastic analysis. After linearization, the proposed controller gains are obtained by solving the linear matrix inequalities. Ultimately, a practical example of the dc motor device is used to illustrate the effectiveness of the proposed new design technique.