Time-Delay Luenberger Observer Design for Sliding Mode Control of Nonlinear Markovian Jump Systems via Event-Triggered Mechanism

Cheng, Min; Zhang, Chunyang; Qiu, Jin; Wu, Zhengtian; Gao, Qing

doi:10.3390/machines9110259

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Time-Delay Luenberger Observer Design for Sliding Mode Control of Nonlinear Markovian Jump Systems via Event-Triggered Mechanism

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School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, China

School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China

School of Electronic and Information Engineering, Suzhou University of Science and Technology, Suzhou 215009, China

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Institute for Automatic Control and Complex Systems (AKS), University of Duisburg-Essen, 47057 Duisburg, Germany

Author to whom correspondence should be addressed.

Academic Editors: Christoph M. Hackl and Hai Wang

Machines 2021, 9(11), 259; https://doi.org/10.3390/machines9110259

Received: 7 August 2021 / Revised: 26 October 2021 / Accepted: 27 October 2021 / Published: 30 October 2021

(This article belongs to the Special Issue Feature Papers to Celebrate the First Impact Factor of Machines)

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Abstract

This paper is focused on the stabilization of Takagi–Sugeno fuzzy model-based Markovian jump systems with the aid of a delayed state observer. Due to network-induced constraints in the communication channel, a delay partition method combined with an event-triggered mechanism is proposed to design the observer. Then, a novel integral sliding surface is designed, based on which sliding mode dynamics is obtained. Further, according to stochastic stability theory, feasible conditions are provided to ensure the sliding mode dynamics and the error dynamics have an H_∞ attenuate level γ. The challenge is to deal with the issue that transition rates may be totally unknown. Moreover, an observer-based sliding mode controller is constructed to ensure the finite-time reachability of the predefined sliding surface. Finally, a numerical example based on a robotic manipulator is given to verify the effectiveness of the proposed method. View Full-Text

Keywords: Markovian jump systems; sliding mode control; observer design; event-triggering scheme

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MDPI and ACS Style

Cheng, M.; Zhang, C.; Qiu, J.; Wu, Z.; Gao, Q. Time-Delay Luenberger Observer Design for Sliding Mode Control of Nonlinear Markovian Jump Systems via Event-Triggered Mechanism. Machines 2021, 9, 259. https://doi.org/10.3390/machines9110259

AMA Style

Cheng M, Zhang C, Qiu J, Wu Z, Gao Q. Time-Delay Luenberger Observer Design for Sliding Mode Control of Nonlinear Markovian Jump Systems via Event-Triggered Mechanism. Machines. 2021; 9(11):259. https://doi.org/10.3390/machines9110259

Chicago/Turabian Style

Cheng, Min, Chunyang Zhang, Jin Qiu, Zhengtian Wu, and Qing Gao. 2021. "Time-Delay Luenberger Observer Design for Sliding Mode Control of Nonlinear Markovian Jump Systems via Event-Triggered Mechanism" Machines 9, no. 11: 259. https://doi.org/10.3390/machines9110259

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Time-Delay Luenberger Observer Design for Sliding Mode Control of Nonlinear Markovian Jump Systems via Event-Triggered Mechanism

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