Robust Control for Discrete-Time Singular Marovian Jump Systems with Partly Unknown Transition Rates

Yuhong Liu; Hui Li; Qishui Zhong; Shouming Zhong

doi:doi:10.11648/j.sjams.20160405.14

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Robust Control for Discrete-Time Singular Marovian Jump Systems with Partly Unknown Transition Rates

Yuhong Liu, Hui Li, Qishui Zhong, Shouming Zhong

Published in Science Journal of Applied Mathematics and Statistics (Volume 4, Issue 5)

Received: 19 September 2016 Accepted: Published: 23 September 2016

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Abstract

This study investigates the problem of robust control for a class of discrete-time singular Marovian jump systems with partly unknown transition rates. Linear matrix inequality (LMI)-based sufficient conditions for the stochastic stability and robust control are developed. Then, a static output feedback controller and a robust static output feedback controller are designed to make sure the closed-loop systems are piecewise regular, causal and stochastically stable. Finally, numerical examples are presented to demonstrate the effectiveness and advantages of the theoretical results.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 4, Issue 5)
DOI	10.11648/j.sjams.20160405.14
Page(s)	217-224
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Robust Control, Partly Unknown Transition Rates, Singular Markovian Jump Systems

References

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APA Style

Yuhong Liu, Hui Li, Qishui Zhong, Shouming Zhong. (2016). Robust Control for Discrete-Time Singular Marovian Jump Systems with Partly Unknown Transition Rates. Science Journal of Applied Mathematics and Statistics, 4(5), 217-224. https://doi.org/10.11648/j.sjams.20160405.14

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ACS Style

Yuhong Liu; Hui Li; Qishui Zhong; Shouming Zhong. Robust Control for Discrete-Time Singular Marovian Jump Systems with Partly Unknown Transition Rates. Sci. J. Appl. Math. Stat. 2016, 4(5), 217-224. doi: 10.11648/j.sjams.20160405.14

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AMA Style

Yuhong Liu, Hui Li, Qishui Zhong, Shouming Zhong. Robust Control for Discrete-Time Singular Marovian Jump Systems with Partly Unknown Transition Rates. Sci J Appl Math Stat. 2016;4(5):217-224. doi: 10.11648/j.sjams.20160405.14

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@article{10.11648/j.sjams.20160405.14,
  author = {Yuhong Liu and Hui Li and Qishui Zhong and Shouming Zhong},
  title = {Robust Control for Discrete-Time Singular Marovian Jump Systems with Partly Unknown Transition Rates},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {4},
  number = {5},
  pages = {217-224},
  doi = {10.11648/j.sjams.20160405.14},
  url = {https://doi.org/10.11648/j.sjams.20160405.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20160405.14},
  abstract = {This study investigates the problem of robust control for a class of discrete-time singular Marovian jump systems with partly unknown transition rates. Linear matrix inequality (LMI)-based sufficient conditions for the stochastic stability and robust control are developed. Then, a static output feedback controller and a robust static output feedback controller are designed to make sure the closed-loop systems are piecewise regular, causal and stochastically stable. Finally, numerical examples are presented to demonstrate the effectiveness and advantages of the theoretical results.},
 year = {2016}
}

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TY  - JOUR
T1  - Robust Control for Discrete-Time Singular Marovian Jump Systems with Partly Unknown Transition Rates
AU  - Yuhong Liu
AU  - Hui Li
AU  - Qishui Zhong
AU  - Shouming Zhong
Y1  - 2016/09/23
PY  - 2016
N1  - https://doi.org/10.11648/j.sjams.20160405.14
DO  - 10.11648/j.sjams.20160405.14
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 217
EP  - 224
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20160405.14
AB  - This study investigates the problem of robust control for a class of discrete-time singular Marovian jump systems with partly unknown transition rates. Linear matrix inequality (LMI)-based sufficient conditions for the stochastic stability and robust control are developed. Then, a static output feedback controller and a robust static output feedback controller are designed to make sure the closed-loop systems are piecewise regular, causal and stochastically stable. Finally, numerical examples are presented to demonstrate the effectiveness and advantages of the theoretical results.
VL  - 4
IS  - 5
ER  -

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Author Information

Yuhong Liu

School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu, China
Hui Li

School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu, China
Qishui Zhong

School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu, China
Shouming Zhong

School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China;Key Laboratory for Neuroinformation of Ministry of Education, University of Electronic Science and Technology of China, Chengdu, China

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Plain Text BibTeX RIS

APA Style

Yuhong Liu, Hui Li, Qishui Zhong, Shouming Zhong. (2016). Robust Control for Discrete-Time Singular Marovian Jump Systems with Partly Unknown Transition Rates. Science Journal of Applied Mathematics and Statistics, 4(5), 217-224. https://doi.org/10.11648/j.sjams.20160405.14

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ACS Style

Yuhong Liu; Hui Li; Qishui Zhong; Shouming Zhong. Robust Control for Discrete-Time Singular Marovian Jump Systems with Partly Unknown Transition Rates. Sci. J. Appl. Math. Stat. 2016, 4(5), 217-224. doi: 10.11648/j.sjams.20160405.14

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AMA Style

Yuhong Liu, Hui Li, Qishui Zhong, Shouming Zhong. Robust Control for Discrete-Time Singular Marovian Jump Systems with Partly Unknown Transition Rates. Sci J Appl Math Stat. 2016;4(5):217-224. doi: 10.11648/j.sjams.20160405.14

Copy | Download

@article{10.11648/j.sjams.20160405.14,
  author = {Yuhong Liu and Hui Li and Qishui Zhong and Shouming Zhong},
  title = {Robust Control for Discrete-Time Singular Marovian Jump Systems with Partly Unknown Transition Rates},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {4},
  number = {5},
  pages = {217-224},
  doi = {10.11648/j.sjams.20160405.14},
  url = {https://doi.org/10.11648/j.sjams.20160405.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20160405.14},
  abstract = {This study investigates the problem of robust control for a class of discrete-time singular Marovian jump systems with partly unknown transition rates. Linear matrix inequality (LMI)-based sufficient conditions for the stochastic stability and robust control are developed. Then, a static output feedback controller and a robust static output feedback controller are designed to make sure the closed-loop systems are piecewise regular, causal and stochastically stable. Finally, numerical examples are presented to demonstrate the effectiveness and advantages of the theoretical results.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Robust Control for Discrete-Time Singular Marovian Jump Systems with Partly Unknown Transition Rates
AU  - Yuhong Liu
AU  - Hui Li
AU  - Qishui Zhong
AU  - Shouming Zhong
Y1  - 2016/09/23
PY  - 2016
N1  - https://doi.org/10.11648/j.sjams.20160405.14
DO  - 10.11648/j.sjams.20160405.14
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 217
EP  - 224
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20160405.14
AB  - This study investigates the problem of robust control for a class of discrete-time singular Marovian jump systems with partly unknown transition rates. Linear matrix inequality (LMI)-based sufficient conditions for the stochastic stability and robust control are developed. Then, a static output feedback controller and a robust static output feedback controller are designed to make sure the closed-loop systems are piecewise regular, causal and stochastically stable. Finally, numerical examples are presented to demonstrate the effectiveness and advantages of the theoretical results.
VL  - 4
IS  - 5
ER  -

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