A State Estimation <i>H<sub>∞</sub></i> Issue for Continuous-Time Impulsive Genetic Regulatory Networks with Random Delays Via Sampled-Data Approach

Pandiselvi Selvakumar; Meenakshi Ramachandran

doi:doi:10.11648/j.acm.20251401.12

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A State Estimation H_∞ Issue for Continuous-Time Impulsive Genetic Regulatory Networks with Random Delays Via Sampled-Data Approach

Pandiselvi Selvakumar, Meenakshi Ramachandran^*

Published in Applied and Computational Mathematics (Volume 14, Issue 1)

Received: 20 October 2024 Accepted: 20 November 2024 Published: 3 January 2025

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Abstract

This paper addresses the state-estimation H_∞ problem for continuous-time impulsive genetic regulatory networks (GRNs) with random delays, using a sampled-data approach. Genetic regulatory networks are fundamental in controlling gene expression and protein synthesis, governed by regulatory interactions between transcription factors and mRNA (Messenger Ribonucleic Acid) binding sites. To estimate mRNA and protein concentrations, sampled measurements replace continuous measurements in this framework. We propose a new model that leverages impulsive control strategies to regulate mRNA and protein dynamics under conditions with random delays. The primary contribution of this study is the derivation of sufficient conditions that guaranteeing that impulsive genetic regulatory networks is globally asymptotically stable is derived. By introducing a discontinuous Lyapunov- Krasovskii functional, sufficient stability analysis has been rooted in terms of LMIs: Linear Matrix Inequalities. By applying Wirtinger inequality technique, conservation of the impulsive GRNs system is globally asymptotically stable in the mean- square sense have been diminished greatly. Eventually, a numerical example is given to the feasibility and advantages of the developed results.

Published in	Applied and Computational Mathematics (Volume 14, Issue 1)
DOI	10.11648/j.acm.20251401.12
Page(s)	12-22
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), 2025. Published by Science Publishing Group

Keywords

Genetic Regulatory Networks (GRNs), Robust State Estimation, Random Delays, Impulsive Equation

References

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APA Style

Selvakumar, P., Ramachandran, M. (2025). A State Estimation H∞ Issue for Continuous-Time Impulsive Genetic Regulatory Networks with Random Delays Via Sampled-Data Approach. Applied and Computational Mathematics, 14(1), 12-22. https://doi.org/10.11648/j.acm.20251401.12

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ACS Style

Selvakumar, P.; Ramachandran, M. A State Estimation H∞ Issue for Continuous-Time Impulsive Genetic Regulatory Networks with Random Delays Via Sampled-Data Approach. Appl. Comput. Math. 2025, 14(1), 12-22. doi: 10.11648/j.acm.20251401.12

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AMA Style

Selvakumar P, Ramachandran M. A State Estimation H∞ Issue for Continuous-Time Impulsive Genetic Regulatory Networks with Random Delays Via Sampled-Data Approach. Appl Comput Math. 2025;14(1):12-22. doi: 10.11648/j.acm.20251401.12

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@article{10.11648/j.acm.20251401.12,
  author = {Pandiselvi Selvakumar and Meenakshi Ramachandran},
  title = {A State Estimation H∞ Issue for Continuous-Time Impulsive Genetic Regulatory Networks with Random Delays Via Sampled-Data Approach},
  journal = {Applied and Computational Mathematics},
  volume = {14},
  number = {1},
  pages = {12-22},
  doi = {10.11648/j.acm.20251401.12},
  url = {https://doi.org/10.11648/j.acm.20251401.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20251401.12},
  abstract = {This paper addresses the state-estimation H∞ problem for continuous-time impulsive genetic regulatory networks (GRNs) with random delays, using a sampled-data approach. Genetic regulatory networks are fundamental in controlling gene expression and protein synthesis, governed by regulatory interactions between transcription factors and mRNA (Messenger Ribonucleic Acid) binding sites. To estimate mRNA and protein concentrations, sampled measurements replace continuous measurements in this framework. We propose a new model that leverages impulsive control strategies to regulate mRNA and protein dynamics under conditions with random delays. The primary contribution of this study is the derivation of sufficient conditions that guaranteeing that impulsive genetic regulatory networks is globally asymptotically stable is derived. By introducing a discontinuous Lyapunov- Krasovskii functional, sufficient stability analysis has been rooted in terms of LMIs: Linear Matrix Inequalities. By applying Wirtinger inequality technique, conservation of the impulsive GRNs system is globally asymptotically stable in the mean- square sense have been diminished greatly. Eventually, a numerical example is given to the feasibility and advantages of the developed results.},
 year = {2025}
}

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TY  - JOUR
T1  - A State Estimation H∞ Issue for Continuous-Time Impulsive Genetic Regulatory Networks with Random Delays Via Sampled-Data Approach
AU  - Pandiselvi Selvakumar
AU  - Meenakshi Ramachandran
Y1  - 2025/01/03
PY  - 2025
N1  - https://doi.org/10.11648/j.acm.20251401.12
DO  - 10.11648/j.acm.20251401.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
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PB  - Science Publishing Group
SN  - 2328-5613
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AB  - This paper addresses the state-estimation H∞ problem for continuous-time impulsive genetic regulatory networks (GRNs) with random delays, using a sampled-data approach. Genetic regulatory networks are fundamental in controlling gene expression and protein synthesis, governed by regulatory interactions between transcription factors and mRNA (Messenger Ribonucleic Acid) binding sites. To estimate mRNA and protein concentrations, sampled measurements replace continuous measurements in this framework. We propose a new model that leverages impulsive control strategies to regulate mRNA and protein dynamics under conditions with random delays. The primary contribution of this study is the derivation of sufficient conditions that guaranteeing that impulsive genetic regulatory networks is globally asymptotically stable is derived. By introducing a discontinuous Lyapunov- Krasovskii functional, sufficient stability analysis has been rooted in terms of LMIs: Linear Matrix Inequalities. By applying Wirtinger inequality technique, conservation of the impulsive GRNs system is globally asymptotically stable in the mean- square sense have been diminished greatly. Eventually, a numerical example is given to the feasibility and advantages of the developed results.
VL  - 14
IS  - 1
ER  -

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Author Information

Pandiselvi Selvakumar

Department of Mathematics, Seethalakshmi Achi College for Women, Pallathur, India

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Meenakshi Ramachandran

Department of Mathematics, Seethalakshmi Achi College for Women, Pallathur, India

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Plain Text BibTeX RIS

APA Style

Selvakumar, P., Ramachandran, M. (2025). A State Estimation H∞ Issue for Continuous-Time Impulsive Genetic Regulatory Networks with Random Delays Via Sampled-Data Approach. Applied and Computational Mathematics, 14(1), 12-22. https://doi.org/10.11648/j.acm.20251401.12

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ACS Style

Selvakumar, P.; Ramachandran, M. A State Estimation H∞ Issue for Continuous-Time Impulsive Genetic Regulatory Networks with Random Delays Via Sampled-Data Approach. Appl. Comput. Math. 2025, 14(1), 12-22. doi: 10.11648/j.acm.20251401.12

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AMA Style

Selvakumar P, Ramachandran M. A State Estimation H∞ Issue for Continuous-Time Impulsive Genetic Regulatory Networks with Random Delays Via Sampled-Data Approach. Appl Comput Math. 2025;14(1):12-22. doi: 10.11648/j.acm.20251401.12

Copy | Download

@article{10.11648/j.acm.20251401.12,
  author = {Pandiselvi Selvakumar and Meenakshi Ramachandran},
  title = {A State Estimation H∞ Issue for Continuous-Time Impulsive Genetic Regulatory Networks with Random Delays Via Sampled-Data Approach},
  journal = {Applied and Computational Mathematics},
  volume = {14},
  number = {1},
  pages = {12-22},
  doi = {10.11648/j.acm.20251401.12},
  url = {https://doi.org/10.11648/j.acm.20251401.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20251401.12},
  abstract = {This paper addresses the state-estimation H∞ problem for continuous-time impulsive genetic regulatory networks (GRNs) with random delays, using a sampled-data approach. Genetic regulatory networks are fundamental in controlling gene expression and protein synthesis, governed by regulatory interactions between transcription factors and mRNA (Messenger Ribonucleic Acid) binding sites. To estimate mRNA and protein concentrations, sampled measurements replace continuous measurements in this framework. We propose a new model that leverages impulsive control strategies to regulate mRNA and protein dynamics under conditions with random delays. The primary contribution of this study is the derivation of sufficient conditions that guaranteeing that impulsive genetic regulatory networks is globally asymptotically stable is derived. By introducing a discontinuous Lyapunov- Krasovskii functional, sufficient stability analysis has been rooted in terms of LMIs: Linear Matrix Inequalities. By applying Wirtinger inequality technique, conservation of the impulsive GRNs system is globally asymptotically stable in the mean- square sense have been diminished greatly. Eventually, a numerical example is given to the feasibility and advantages of the developed results.},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - A State Estimation H∞ Issue for Continuous-Time Impulsive Genetic Regulatory Networks with Random Delays Via Sampled-Data Approach
AU  - Pandiselvi Selvakumar
AU  - Meenakshi Ramachandran
Y1  - 2025/01/03
PY  - 2025
N1  - https://doi.org/10.11648/j.acm.20251401.12
DO  - 10.11648/j.acm.20251401.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 12
EP  - 22
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20251401.12
AB  - This paper addresses the state-estimation H∞ problem for continuous-time impulsive genetic regulatory networks (GRNs) with random delays, using a sampled-data approach. Genetic regulatory networks are fundamental in controlling gene expression and protein synthesis, governed by regulatory interactions between transcription factors and mRNA (Messenger Ribonucleic Acid) binding sites. To estimate mRNA and protein concentrations, sampled measurements replace continuous measurements in this framework. We propose a new model that leverages impulsive control strategies to regulate mRNA and protein dynamics under conditions with random delays. The primary contribution of this study is the derivation of sufficient conditions that guaranteeing that impulsive genetic regulatory networks is globally asymptotically stable is derived. By introducing a discontinuous Lyapunov- Krasovskii functional, sufficient stability analysis has been rooted in terms of LMIs: Linear Matrix Inequalities. By applying Wirtinger inequality technique, conservation of the impulsive GRNs system is globally asymptotically stable in the mean- square sense have been diminished greatly. Eventually, a numerical example is given to the feasibility and advantages of the developed results.
VL  - 14
IS  - 1
ER  -

Copy | Download