Finite-Time State Estimation of Switched Neural Networks with Both Time-Varying Delays and Leakage Delay

Fangjing Zheng; Zhifeng Lu

doi:doi:10.11648/j.ajam.20231101.12

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Finite-Time State Estimation of Switched Neural Networks with Both Time-Varying Delays and Leakage Delay

Fangjing Zheng, Zhifeng Lu

Published in American Journal of Applied Mathematics (Volume 11, Issue 1)

Received: 25 December 2022 Accepted: 19 January 2023 Published: 6 February 2023

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Abstract

In this thesis, we deal with the issues of the finite-time state estimation (FTSE) for a set of switched neural networks (SNNs), in which the hybrid effects of time-varying delays and leakage delay are taken into consideration. Therefore, the model of SNNs under discussion is quite comprehensive and more practical. In the light of an applicable piecewise Lyapunov-Krasovskii (L-K) functional which has double integral terms, some novel sufficient criteria are put forward with the average dwell time (ADT) technique, so that the estimation error system is finite-time boundedness (FTB). It is crucial to notice that the estimation results in our work are time-delay dependent, which depend on the leakage delay as well as the upper bound of the time-varying delays. The results show that the unknown gain matrix of the state estimator is achieved by solving a series of linear matrix inequalities (LMIs), which can be effortlessly tested with the MATLAB Toolbox. Moreover, by combining with free weight matrix method in the proof process, the results we obtained do not require the differentiability of time-varying delays any more, which is less conservative than some existing results. Finally, an example is performed with its numerical simulations to corroborate the efficiency of the theoretical results.

Published in	American Journal of Applied Mathematics (Volume 11, Issue 1)
DOI	10.11648/j.ajam.20231101.12
Page(s)	7-16
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

Finite-Time State Estimation, Switched Neural Networks, Time-Varying Delays, Leakage Delay

References

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APA Style

Fangjing Zheng, Zhifeng Lu. (2023). Finite-Time State Estimation of Switched Neural Networks with Both Time-Varying Delays and Leakage Delay. American Journal of Applied Mathematics, 11(1), 7-16. https://doi.org/10.11648/j.ajam.20231101.12

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ACS Style

Fangjing Zheng; Zhifeng Lu. Finite-Time State Estimation of Switched Neural Networks with Both Time-Varying Delays and Leakage Delay. Am. J. Appl. Math. 2023, 11(1), 7-16. doi: 10.11648/j.ajam.20231101.12

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AMA Style

Fangjing Zheng, Zhifeng Lu. Finite-Time State Estimation of Switched Neural Networks with Both Time-Varying Delays and Leakage Delay. Am J Appl Math. 2023;11(1):7-16. doi: 10.11648/j.ajam.20231101.12

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@article{10.11648/j.ajam.20231101.12,
  author = {Fangjing Zheng and Zhifeng Lu},
  title = {Finite-Time State Estimation of Switched Neural Networks with Both Time-Varying Delays and Leakage Delay},
  journal = {American Journal of Applied Mathematics},
  volume = {11},
  number = {1},
  pages = {7-16},
  doi = {10.11648/j.ajam.20231101.12},
  url = {https://doi.org/10.11648/j.ajam.20231101.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20231101.12},
  abstract = {In this thesis, we deal with the issues of the finite-time state estimation (FTSE) for a set of switched neural networks (SNNs), in which the hybrid effects of time-varying delays and leakage delay are taken into consideration. Therefore, the model of SNNs under discussion is quite comprehensive and more practical. In the light of an applicable piecewise Lyapunov-Krasovskii (L-K) functional which has double integral terms, some novel sufficient criteria are put forward with the average dwell time (ADT) technique, so that the estimation error system is finite-time boundedness (FTB). It is crucial to notice that the estimation results in our work are time-delay dependent, which depend on the leakage delay as well as the upper bound of the time-varying delays. The results show that the unknown gain matrix of the state estimator is achieved by solving a series of linear matrix inequalities (LMIs), which can be effortlessly tested with the MATLAB Toolbox. Moreover, by combining with free weight matrix method in the proof process, the results we obtained do not require the differentiability of time-varying delays any more, which is less conservative than some existing results. Finally, an example is performed with its numerical simulations to corroborate the efficiency of the theoretical results.},
 year = {2023}
}

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TY  - JOUR
T1  - Finite-Time State Estimation of Switched Neural Networks with Both Time-Varying Delays and Leakage Delay
AU  - Fangjing Zheng
AU  - Zhifeng Lu
Y1  - 2023/02/06
PY  - 2023
N1  - https://doi.org/10.11648/j.ajam.20231101.12
DO  - 10.11648/j.ajam.20231101.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 7
EP  - 16
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20231101.12
AB  - In this thesis, we deal with the issues of the finite-time state estimation (FTSE) for a set of switched neural networks (SNNs), in which the hybrid effects of time-varying delays and leakage delay are taken into consideration. Therefore, the model of SNNs under discussion is quite comprehensive and more practical. In the light of an applicable piecewise Lyapunov-Krasovskii (L-K) functional which has double integral terms, some novel sufficient criteria are put forward with the average dwell time (ADT) technique, so that the estimation error system is finite-time boundedness (FTB). It is crucial to notice that the estimation results in our work are time-delay dependent, which depend on the leakage delay as well as the upper bound of the time-varying delays. The results show that the unknown gain matrix of the state estimator is achieved by solving a series of linear matrix inequalities (LMIs), which can be effortlessly tested with the MATLAB Toolbox. Moreover, by combining with free weight matrix method in the proof process, the results we obtained do not require the differentiability of time-varying delays any more, which is less conservative than some existing results. Finally, an example is performed with its numerical simulations to corroborate the efficiency of the theoretical results.
VL  - 11
IS  - 1
ER  -

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Author Information

Fangjing Zheng

School of Mathematics and Statistics, Shandong Normal University, Ji’nan, PR China
Zhifeng Lu

School of Mathematics and Statistics, Shandong Normal University, Ji’nan, PR China

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Plain Text BibTeX RIS

APA Style

Fangjing Zheng, Zhifeng Lu. (2023). Finite-Time State Estimation of Switched Neural Networks with Both Time-Varying Delays and Leakage Delay. American Journal of Applied Mathematics, 11(1), 7-16. https://doi.org/10.11648/j.ajam.20231101.12

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ACS Style

Fangjing Zheng; Zhifeng Lu. Finite-Time State Estimation of Switched Neural Networks with Both Time-Varying Delays and Leakage Delay. Am. J. Appl. Math. 2023, 11(1), 7-16. doi: 10.11648/j.ajam.20231101.12

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AMA Style

Fangjing Zheng, Zhifeng Lu. Finite-Time State Estimation of Switched Neural Networks with Both Time-Varying Delays and Leakage Delay. Am J Appl Math. 2023;11(1):7-16. doi: 10.11648/j.ajam.20231101.12

Copy | Download

@article{10.11648/j.ajam.20231101.12,
  author = {Fangjing Zheng and Zhifeng Lu},
  title = {Finite-Time State Estimation of Switched Neural Networks with Both Time-Varying Delays and Leakage Delay},
  journal = {American Journal of Applied Mathematics},
  volume = {11},
  number = {1},
  pages = {7-16},
  doi = {10.11648/j.ajam.20231101.12},
  url = {https://doi.org/10.11648/j.ajam.20231101.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20231101.12},
  abstract = {In this thesis, we deal with the issues of the finite-time state estimation (FTSE) for a set of switched neural networks (SNNs), in which the hybrid effects of time-varying delays and leakage delay are taken into consideration. Therefore, the model of SNNs under discussion is quite comprehensive and more practical. In the light of an applicable piecewise Lyapunov-Krasovskii (L-K) functional which has double integral terms, some novel sufficient criteria are put forward with the average dwell time (ADT) technique, so that the estimation error system is finite-time boundedness (FTB). It is crucial to notice that the estimation results in our work are time-delay dependent, which depend on the leakage delay as well as the upper bound of the time-varying delays. The results show that the unknown gain matrix of the state estimator is achieved by solving a series of linear matrix inequalities (LMIs), which can be effortlessly tested with the MATLAB Toolbox. Moreover, by combining with free weight matrix method in the proof process, the results we obtained do not require the differentiability of time-varying delays any more, which is less conservative than some existing results. Finally, an example is performed with its numerical simulations to corroborate the efficiency of the theoretical results.},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - Finite-Time State Estimation of Switched Neural Networks with Both Time-Varying Delays and Leakage Delay
AU  - Fangjing Zheng
AU  - Zhifeng Lu
Y1  - 2023/02/06
PY  - 2023
N1  - https://doi.org/10.11648/j.ajam.20231101.12
DO  - 10.11648/j.ajam.20231101.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 7
EP  - 16
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20231101.12
AB  - In this thesis, we deal with the issues of the finite-time state estimation (FTSE) for a set of switched neural networks (SNNs), in which the hybrid effects of time-varying delays and leakage delay are taken into consideration. Therefore, the model of SNNs under discussion is quite comprehensive and more practical. In the light of an applicable piecewise Lyapunov-Krasovskii (L-K) functional which has double integral terms, some novel sufficient criteria are put forward with the average dwell time (ADT) technique, so that the estimation error system is finite-time boundedness (FTB). It is crucial to notice that the estimation results in our work are time-delay dependent, which depend on the leakage delay as well as the upper bound of the time-varying delays. The results show that the unknown gain matrix of the state estimator is achieved by solving a series of linear matrix inequalities (LMIs), which can be effortlessly tested with the MATLAB Toolbox. Moreover, by combining with free weight matrix method in the proof process, the results we obtained do not require the differentiability of time-varying delays any more, which is less conservative than some existing results. Finally, an example is performed with its numerical simulations to corroborate the efficiency of the theoretical results.
VL  - 11
IS  - 1
ER  -

Copy | Download