Abstract
This paper addresses the asynchronous robust \(H_{\infty }\) dynamic output feedback control for Takagi–Sugeno fuzzy uncertain stochastic Markov jump systems with time-varying delays. The modes of devised fuzzy controller run asynchronously with the modes of controlled plant, which is described through a hidden Markov model. Dynamic output feedback control is that the output feedback only takes the output signal that the object can detect as the feedback signal. Because the measurement output is local information, the feedback is also local. Although it is feasible, it cannot reflect the overall situation. The fuzzy dynamic output feedback adopts parallel distribution compensation technique, which can realize global feedback, but realizing this feedback control is full of difficulties and challenges. And although introducing more variables can make the condition less conservative, it also increases the number of linear matrix inequalities and computational complexity. Improved conditions are acquired to ensure the robust exponential mean-square stability and \(H_{\infty }\) performance index for the closed-loop fuzzy uncertain stochastic Markov jump systems. Based on exponential mean-square stability, the asynchronous fuzzy dynamic output feedback controller is realized in terms of linear matrix inequalities. A numerical example and a single-link robot arm are employed to show the effectiveness and correctness of the method proposed in this paper.
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Acknowledgements
The authors would like to thank the Editors and the Referees for carefully reading the paper and for the comments which have helped us to greatly improve the paper. This work was supported by the National Natural Science Foundation of China under Grant Nos. 62173174, 61773191, 61973148, 62003154; Support Plan for Outstanding Youth Innovation Team in Shandong Higher Education Institutions under Grant 2019KJI010; the Natural Science Foundation of Shandong Province for Key Projects under Grant ZR2020KA010; Graduate education high-quality curriculum construction project for Shandong Province under Grant SDYKC20185.
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Lin, Y., Zhuang, G., Xia, J. et al. Asynchronous Dynamic Output Feedback Control for Delayed Fuzzy Stochastic Markov Jump Systems Based on HMM Strategy. Int. J. Fuzzy Syst. 24, 2302–2317 (2022). https://doi.org/10.1007/s40815-022-01273-4
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DOI: https://doi.org/10.1007/s40815-022-01273-4