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Robust interval stability/stabilization and H∞ feedback control for uncertain stochastic Markovian jump systems based on the linear operator

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Abstract

This paper focuses on the problem of robust H∞ state feedback control with interval pole constraints for uncertain stochastic Markovian jump systems (MJSs). First, we present the sufficient conditions of robust interval stability using a linear operator and its spectrum. A robust interval stabilization controller is designed for MJSs; it ensures the stability of MJSs and adjusts the rate of convergence. In addition, the robust H∞ controller with interval pole constraints is designed with the admissible parametric uncertainties and a prescribed H∞ disturbance attenuation level; this guarantees that the closed-loop system is robust and asymptotically stable with an ideal rate of convergence. A numerical example is provided to demonstrate the effectiveness of the proposed method.

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Acknowledgements

This work was partially supported by Natural Science Foundation of Shandong Province (Grant No. ZR2018MF028), National Natural Science Foundation of China (Grant Nos. 61773191, 61973148, 61673169), Support Plan for Outstanding Youth Innovation Team in Shandong Higher Education Institutions (Grant No. 2019KJI010), Undergraduate Education Reform Project of Higher Education in Shandong Province (Grant No. M2018X047), and Liaocheng University Education Reform Project Foundation (Grant Nos. G201811, 26322170267). We greatly appreciate anonymous reviewers for their constructive suggestions and comments on the improvement of the paper.

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Authors and Affiliations

  1. School of Mathematics Science, Liaocheng University, Liaocheng, 252000, China

    Huasheng Zhang, Jianwei Xia & Guangming Zhuang

  2. School of Electrical and Information Engineering, Anhui University of Technology, Maanshan, 243002, China

    Hao Shen

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  1. Huasheng Zhang
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  2. Jianwei Xia
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  3. Guangming Zhuang
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  4. Hao Shen
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Correspondence to Jianwei Xia or Hao Shen.

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Zhang, H., Xia, J., Zhuang, G. et al. Robust interval stability/stabilization and H∞ feedback control for uncertain stochastic Markovian jump systems based on the linear operator. Sci. China Inf. Sci. 65, 142202 (2022). https://doi.org/10.1007/s11432-020-3087-1

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  • DOI: https://doi.org/10.1007/s11432-020-3087-1

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