Paper:

# 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

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.20 No.7, pp. 1094-1102, 2016.

- [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] 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] 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] 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] I. Shmulevich, E. R. Dougherty, and W. Zhang, “Gene perturbation and intervention in probabilistic Boolean networks,” Bioinformatics, Vol.18, pp. 1319-1331, 2002.
- [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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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.