Skip to main content
SpringerLink
Log in

Robust Passivity Analysis of Stochastic Genetic Regulatory Networks with Levy Noise

  • Regular Papers
  • Control Theory and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

Robust passivity analysis for stochastic genetic regulatory networks (GRNs) with time-varying delays and Levy noise is addressed in this paper. The main objective is to estimate the true concentrations of mRNA and proteins using the available measured outputs. To analyze the passivity performance for stochastic GRNs a new set of delay-dependent conditions are established with the help of Lyapunov-Krasovskii Functional (LKF), some integral inequalities and free-weighting matrix approach. Further, the results are also extended to analyze the performance of passivity in the presence of uncertainties. The sufficient conditions are expressed as linear matrix inequalities (LMIs), which can be easily solved by Matlab software. Finally, a numerical example is given to demonstrate the usefulness of the proposed model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. F. Wu, “Global and robust stability analysis of genetic regulatory networks with time-varying delays and parameter uncertainties,” IEEE Transactions on Biomedical Circuits and Systems, vol. 5, no. 4, pp. 391–398, August 2011.

    Article  Google Scholar 

  2. Z. Wang, X. Liao, S. Guo, and G. Liu, “Stability analysis of genetic regulatory network with time delays and parameter uncertainties,” IET Control Theory and Applications, vol. 4, no. 10, pp. 2018–2028, October 2010.

    Article  MathSciNet  Google Scholar 

  3. Q. Zhou, X. Shao, H. R. Karimi, and J. Zhu, “Stability of genetic regulatory networks with time-varying delays: Delta operator method,” Neurocomputing, vol. 149, no. 3, pp. 490–495, February 2015.

    Article  Google Scholar 

  4. P. L. Liu, “Robust stability analysis of genetic regulatory network with time delays,” ISA Transactios, vol. 52, no. 3, pp. 326–334, May 2013.

    Article  Google Scholar 

  5. C. Li, L. Chen, and K. Aihara, “Stability of genetic networks with SUM regulatory logic: Lure systems and LMI approach,” IEEE Transactions on Circuits and Systems-I, vol. 53, no. 11, pp. 2451–2458, November 2006.

    Article  MathSciNet  Google Scholar 

  6. F. Ren and J. Cao, “Asymptotic and robust stability of genetic regulatory networks with time-varying delays,” Neurocomputing, vol. 71, no. 4–6, pp. 834–842, January 2008.

    Article  Google Scholar 

  7. Z. Li, D. Chen, Y. Liu, and Y. Zhao, “New delay dependent stability criteria of genetic regulatory networks subject to time-varying delays,” Neurocomputing, vol. 207, pp. 763–771, September 2016.

    Article  Google Scholar 

  8. Y. Wang, A. Yu, and X. Zhang, “Robust stability of stochastic genetic regulatory networks with time-varying delays: A delay fractioning approach,” Neural Computing and Applications, vol. 23, pp. 1217–1227, July 2013.

    Article  Google Scholar 

  9. H. Wu, X. Liao, S. Guo, W. Feng, and Z. Wang, “Stochastic stability for uncertain genetic regulatory networks with interval time-varying delays,” Neurocomputing, vol. 72, no. 13–15, pp. 3262–3276, August 2009.

    Google Scholar 

  10. Z. Li and K. Chen, “Exponential stability of stochastic genetic regulatory networks with interval uncertainties and multiple delays,” Arabian Journal for Science and Engineering, vol. 39, pp. 6507–6520, June 2014.

    Article  MathSciNet  Google Scholar 

  11. Z. P. Luo, H. L. Yang, and J. Cao, “Stability of genetic regulatory networks based on switched systems and mixed time-delays,” Mathematical Biosciences, vol. 278, pp. 94–99, June 2016.

    Article  MathSciNet  Google Scholar 

  12. D. Zhang and L. Yu, “Passivity analysis for stochastic Markovian switching genetic regulatory networks with time-varying delays,” Communication in Nonlinear Science and Numerical Simulation, vol. 16, no. 8, pp. 2985–2992, August 2011.

    Article  MathSciNet  Google Scholar 

  13. K. Mathiyalagan, R. Sakthivel, and S. M. Anthoni, “New robust passivity criteria for discrete-time genetic regulatory networks with Markovian jumping parameters,” Canadian Journal of Physics, vol. 90, no. 2, pp. 107–118, February 2012.

    Article  Google Scholar 

  14. C. Sowmiya, R. Raja, J. Cao, R. P. Agarwal, and G. Rajchakit, “Passivity analysis for uncertain BAM neural networks with leakage, discrete and distributed delays using novel summation inequality,” International Journal of Control, Automation, and Systems, vol. 17, pp. 2114–2124, July 2019.

    Article  Google Scholar 

  15. T. H. Lee, M. J. Park, O. M. Kwon, J. H. Park, and S. M. Lee, “State estimation for genetic regulatory networks with time-varying delay using stochastic sampled data,” Proc. of 9th Asian Control Conference, pp. 1–6, 2013.

  16. W. Chen, D. Chen, J. Hu, J. Liang, and A. M. Dobaie, “A sampled-data approach to robust H∞ state estimation for genetic regulatory networks with random delays,” International Journal of Control, Automation, and Systems, vol. 16, no. 3–4, pp. 491–504, January 2018.

    Article  Google Scholar 

  17. J. Wang, H. Wang, H. Shen, B. Wang, and J. H. Park, “Finite-time H∞ state estimation for PDT switched genetic regulatory networks with randomly occurring uncertainties,” IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 19, no. 3, pp. 1651–1660, 2022.

    Google Scholar 

  18. Z. M. Li, X. H. Chang, X. K. Du, and L. Yu, “H∞ control of discrete-time uncertain linear systems with quantized feedback,” Neurocomputing, vol. 174, pp. 790–794, January 2016.

    Article  Google Scholar 

  19. B. Oksendal, Stochastic Differential Equations, 5th ed., Springer-Verlag, NewYork, 2003.

    Book  Google Scholar 

  20. H. Zhang, J. Xia, H. Shen, B. Zhang, and Z. Wang, “Pth moment regional stability/stabilization and generalized pole assignment of linear stochastic systems: Based on the generalized H-representation method,” International Journal of Robust Nonlinear Control, vol. 65, no. 3, p. 139202, March 2020.

    Google Scholar 

  21. D. Applebaum, Levy Processes and Stochastic Calculus, Cambridge University Press, 2009.

  22. J. Bertoin, Levy Processes, Cambridge University Press, 1996.

  23. X. Chen, F. Wu, J. Duan, J. Kurths, and X. Li, “Mostprobable dynamics of a genetic regulatory network under stable Levy noise,” Applied Mathematics and Computation, vol. 348, no. 1, pp. 425–436, May 2019.

    Article  MathSciNet  Google Scholar 

  24. F. Wu, X. Chen, Y. Zheng, J. Duan, J. Kurths, and X. Li, “Levy noise induced transition and enhanced stability in a gene regulatory network,” Chaos, vol. 28, no. 7, p. 075510, July 2018.

    Article  MathSciNet  Google Scholar 

  25. Y. Zheng, L. Serdukova, J. Duan, and J. Kurths, “Transitions in genetic transcriptional regulatory system under Levy motion,” Scientific Reports, vol. 6, no. 1, pp. 1–12, July 2018.

    Google Scholar 

  26. Q. Luo, Y. Gong, and C. Jia, “Stability of gene regulatory networks with Levy noise,” Science China Information Science, vol. 60, no. 1, p. 072264, July 2017.

    Google Scholar 

  27. Y. Guo, T. Yao, L. Wang, and J. Tan, “Levy noise induced transition and stochastic resonance in a tumor growth model,” Applied Mathematical Modelling, vol. 94, pp. 506–516, January 2021.

    Article  MathSciNet  Google Scholar 

  28. J. Wu, “Stability of a three species stochastic delay predator-prey system with Levy noise,” Physica A: Statistical Mechanics and its Applications, vol. 502, pp. 492–505, July 2018.

    Article  MathSciNet  Google Scholar 

  29. H. Dong, M. Luo, and M. Xiao, “Synchronization for stochastic coupled networks with Levy noise via event-triggered control,” Neural Networks, vol. 141, pp. 40–51, March 2021.

    Article  Google Scholar 

  30. G. M. Church, H. L. He, and T. Chen, “Modeling gene expression with differential equations,” Proc. of the 4th Pacific Symposium on Biocomputing, USA, 1999.

  31. H. Wu, X. Liao, W. Feng, S. Guo, and W. Zhang, “Robust stability for uncertain genetic regulatory networks with interval time-varying delays,” Information Sciences, vol. 180, no. 18, pp. 3532–3545, September 2010.

    Article  MathSciNet  Google Scholar 

  32. Z. Feng and J. Lam, “Integral partitioning approach to robust stabilization for uncertain distributed time-delay systems,” International Journal of Robust and Nonlinear Control, vol. 22, no. 6, pp. 676–689, April 2012.

    Article  MathSciNet  Google Scholar 

  33. Y. Wang, L. Xie, and C. E. De Souza, “Robust control of a class of uncertain nonlinear system,” Systems & Control Letters, vol. 19, no. 2, pp. 139–149, August 1992.

    Article  MathSciNet  Google Scholar 

  34. Z. Wang, S. Lauria, J. Fang, and X. Liu, “Exponential stability of uncertain stochastic neural networks with mixed time-delays,” Chaos, Solitons & Fractals, vol. 32, no. 1, pp. 62–72, April 2007.

    Article  MathSciNet  Google Scholar 

  35. D. Zhang, G. Feng, Y. Shi, and D. Srinivasan, “Physical safety and cyber security analysis of multi-agent systems: A survey of recent advances,” IEEE/CAA Journal of Automatica Sinica, vol. 8, no. 2, pp. 319–333, February 2021.

    Article  MathSciNet  Google Scholar 

  36. D. Zhang, Q. G. Wang, G. Feng, Y. Shi, and A. V. Vasilakos, “A survey on attack detection estimation and control of industrial cyber-physical systems,” ISA Transactions, vol. 116, pp. 1–16, 2021.

    Article  Google Scholar 

  37. Z. Ye, D. Zhang, and Z. G. Wu, “Adaptive event-based tracking control of unmanned marine vehicle systems with DoS attack,” Journal of the Franklin Institute, vol. 358, pp. 1915–1939, January 2021.

    Article  MathSciNet  Google Scholar 

  38. M. Elowitz and S. Leibler, “A synthetic oscillatory network of transcriptional regulators,” Nature, vol. 403, no. 1, pp. 335–338, January 2000.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. PSG College of Technology, Coimbatore, 641004, India

    Palraj Jothiappan

  2. Department of Mathematics, Bharathiar University, Coimbatore, 641046, India

    Mathiyalagan Kalidass

Authors
  1. Palraj Jothiappan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mathiyalagan Kalidass
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mathiyalagan Kalidass.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Palraj Jothiappan received his B.Sc. and M.Sc. degrees in mathematics from Bharathiar University, Coimbatore, in 2007 and 2009, respectively. He was awarded his M.Phil. and Ph.D. degrees in mathematics from Bharathiar University, Coimbatore, in 2010 and 2016, respectively. Currently he is working as an Assistant Professor, Department of Mathematics, PSG College of Technology, Coimbatore. To his credit, he has published 5 research papers in reputed journals. His current research interests include finite element analysis, partial differential equations, and robust control for nonlinear systems.

Mathiyalagan Kalidass received his B.Sc., M.Sc., and M.Phil. degrees in mathematics from Bharathiar University, Coimbatore, India, in 2005, 2007, and 2008, respectively. He was awarded a Ph.D. degree in mathematics from Anna University, Chennai, India, in 2012. He was a Senior Engineering Research Fellow and CSIR Senior Research Fellow in the Department of Mathematics, Anna university of Technology, Coimbatore, India from June 2009 to December 2012. He was a Post-Doctoral Research Fellow in the Institute of Cyber-System and Control, Zhejiang University, China in 2013. He worked as Post-Doctoral Research Associate and Research Professor in Department of Electrical Engineering, Yeungnam University, Korea. Then he joined as Dr. D. S. Kothari postdoctoral fellow of University Grants Commission, India in the Department of Mathematics, Bharathiar University, Coimbatore, India. Currently he is working as an Assistant Professor in the Department of Mathematics, Bharathiar University, Coimbatore, India. His current research interests include control theory and its applications for ordinary and partial differential equations, time delay systems. He serves as an Associate Editor in International Journal of Control, Automation, and Systems and Academic Editor in Mathematical Problems in Engineering. He is a recipient of the Highly Cited Researcher Award by Clarivate Analytics (formerly, Thomson Reuters) in 2019.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jothiappan, P., Kalidass, M. Robust Passivity Analysis of Stochastic Genetic Regulatory Networks with Levy Noise. Int. J. Control Autom. Syst. 20, 3241–3251 (2022). https://doi.org/10.1007/s12555-021-0552-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-021-0552-8

Keywords

Search

Navigation