Top > JACIII > Robust Stability of Discrete-Time Randomly Switched Delayed Ge ...

single-jc.php

JACIII Vol.20 No.7 pp. 1094-1102
doi: 10.20965/jaciii.2016.p1094
(2016)

Paper:

Views over last 60 days: 765

Robust Stability of Discrete-Time Randomly Switched Delayed Genetic Regulatory Networks with Known Sojourn Probabilities

Xiongbo Wan, Chuanyu Ren, and Jianqi An

School of Automation, China University of Geosciences
Wuhan 430074, China

Received:
July 6, 2016
Accepted:
September 18, 2016
Published:
December 20, 2016
Creative Commons License
Keywords:
genetic regulatory networks (GRNs), known sojourn probabilities, discrete Wirtinger-based inequality, linear matrix inequalities (LMIs)
Abstract
This study investigates stability problems related to discrete-time randomly switched genetic regulatory networks (GRNs) with time-varying delays. A new discrete-time randomly switched GRN model with known sojourn probabilities is proposed. By utilizing the discrete Wirtinger-based inequality and a newly proposed constraint condition on the feedback regulatory function, which have not been fully used in stability analysis of discrete-time GRNs, we establish delay-dependent stability and robust stability criteria. These criteria possess the sojourn probabilities of randomly switched GRNs. Two numerical examples are provided to demonstrate the effectiveness of the established results.
Cite this article as:
X. Wan, C. Ren, and J. An, “Robust Stability of Discrete-Time Randomly Switched Delayed Genetic Regulatory Networks with Known Sojourn Probabilities,” J. Adv. Comput. Intell. Intell. Inform., Vol.20 No.7, pp. 1094-1102, 2016.
Data files:
References
  1. [1] X. Wan, L. Xu, H. Fang, and G. Ling, “Robust non-fragile H∞ state estimation for discrete-time genetic regulatory networks with Markov jump delays and uncertain transition probabilities,” Neurocomputing, Vol.154, pp. 162-173, 2015.
  2. [2] Q. Zhou, and X. Shao, “Stability of genetic regulatory networks with time-varying delay: Delta operator method,” Neurocomputing, Vol.149, pp. 490-495, 2015.
  3. [3] I. Ivanov and E. R. Dougherty, “Modelling genetic regulatory networks: continuous or discrete,” J. Biol. Syst., Vol.14, No.2, pp. 219-229, 2006.
  4. [4] J. Liang and J. Lam, “Robust state estimation for stochastic genetic regulatory networks,” Int. J. Syst. Sci., Vol.41, No.1, pp. 47-63, 2010.
  5. [5] I. Shmulevich, E. R. Dougherty, and W. Zhang, “Gene perturbation and intervention in probabilistic Boolean networks,” Bioinformatics, Vol.18, pp. 1319-1331, 2002.
  6. [6] P. Smolen, D.A. Baxter, and J. H. Byrne, “Mathematical modeling of gene networks,” Neuron., Vol.26, No.3, pp. 567-580, 2000.
  7. [7] H. J. De, “Modeling and simulation of genetic regulatory systems: a literature review,” J. Comput. Biol., Vol.9, No.1, pp. 67-103, 2002.
  8. [8] R. Coutinho, B. Fernandez, R. Lima, et al., “Discrete-time piecewise affine models of genetic regulatory networks,” J. Math. Biol., Vol.52, No.4, pp. 524-570, 2006.
  9. [9] X. Wan, L. Xu, H. Fang, F. Yang, and X. Li, “Exponential synchronization of switched genetic oscillators with time-varying delays,” J. Frankl. Inst., Vol.351, No.8, pp. 4395-4414, 2014.
  10. [10] Y. Sun, G. Feng, and J. Cao, “Stochastic stability of Markovian switching genetic regulatory networks,” Phys. Lett. A, Vol.373, No.18-19, pp. 1646-1652, 2009.
  11. [11] X. Li, R. Rakkiyappan, and C. Pradeep, “Robust μ - stability analysis of Markovian switching uncertain stochastic genetic regulatory networks with unbounded time-varying delays,” Commun. Nonlinear Sci. Numer. Simul., Vol.17, No.10, pp. 3894-3905, 2012.
  12. [12] J. Liang, J. Lam, and Z. Wang, “State estimation for Markov-type genetic regulatory networks with delays and uncertain mode transition rates,” Phys. Lett. A, Vol.373, No.47, pp. 4328-4337, 2009.
  13. [13] P. Balasubramaniam, R. Rakkiyappan, and R. Krishnasamy, “Stochastic stability of Markovian jumping uncertain stochastic genetic regulatory networks with interval time-varying delays,” Math. Biosci., Vol.226, No.2, pp. 97-108, 2010.
  14. [14] E. Tian, D. Yue, and T. Yang, “Analysis and synthesis of randomly switched systems with known sojourn probabilities,” Inform. Sci., Vol.277, pp. 481-491, 2014.
  15. [15] E. Tian, W.K. Wong, and D. Yue, “Robust control for switched systems with input delays: A sojourn-probability-dependent method,” Inform. Sci., Vol.283, pp. 22-35, 2014.
  16. [16] Y. Yao, J. Liang, and J. Cao, “Stability analysis for switched genetic regulatory networks: an average dwell time approach,” J. Frankl. Inst., Vol.348, No.10, pp. 2718-2733, 2011.
  17. [17] W. Zhang, J. Fang, and W. Cui, “Exponential stability of switched genetic regulatory networks with both stable and unstable subsystems,” J. Frankl. Inst., Vol.350, No.8, pp. 2322-2333, 2013.
  18. [18] X. Wan, C. Ren, J. An, et al., “Stability analysis for discrete-time genetic regulatory networks with time-varying delays using discrete Wirtinger-based inequality,” The 35th Chinese Control Conf., Chengdu, China, pp. 1572-1577, 2016.
  19. [19] J. Cao and F. Ren, “Exponential stability of discrete-time genetic regulatory net-works with delays,” IEEE Trans. Neural Netw., Vol.19, No.3, pp. 520-523, 2008.
  20. [20] D. Zhang, H. Song, L. Yu, et al., “Set-values filtering for discrete time-delay genetic regulatory networks with time-varying parameters,” Nonlinear Dyn., Vol.69, No.1-2, pp. 693-703, 2012.
  21. [21] P. T. Nam, P. N. Pathirana, and H. Trinh, “Discrete Wirtinger-based inequality and its application,” J. Frankl. Inst., Vol.352, pp. 1893-1905, 2015.
  22. [22] X. Wan, L. Xu, H. Fang, and F. Yang, “Robust stability analysis for discrete-time genetic regulatory networks with probabilistic time delays,” Neurocomputing, Vol.124, pp. 72-80, 2014.
  23. [23] Q. Ma, S. Xu, Y. Zou, and J. Lu, “Robust stability for discrete-time stochastic genetic regulatory networks,” Nonlinear Anal.: Real World Appl., Vol.12, pp. 2586-2595, 2011.

Creative Commons License  This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

*This site is desgined based on HTML5 and CSS3 for modern browsers, e.g. Chrome, Firefox, Safari, Edge, Opera.

Last updated on Sep. 09, 2024