New results on asymptotic and robust stability of genetic regulatory networks with time-varying delays

International Journal of Innovative Computing, Information and Control

Volumn 8, Issue 4, 2012, Pages 2889-2900

  Yan, Ruixia ^a   Liu, Jinliang ^b  

^a DONGHUA UNIVERSITY   (China)

^b NANJING UNIVERSITY OF FINANCE AND ECONOMICS   (China)

Author keywords

Genetic regulatory networks; Linear matrix inequality (LMI); Piecewise analysis method; Time varying delays

Indexed keywords

ANALYSIS METHOD; ANALYSIS RESULTS; CONVEXITY PROPERTIES; FREE-WEIGHTING MATRIX METHOD; GENETIC NETWORKS; GENETIC REGULATORY NETWORKS; LINEAR MATRIX INEQUALITY (LMI); LINEAR MATRIX INEQUALITY (LMIS); LINEAR MATRIX INEQUALITY TECHNIQUES; LYAPUNOV FUNCTIONALS; MATRIX INEQUALITY; NEW RESULTS; PIECE-WISE; ROBUST ASYMPTOTIC STABILITY; ROBUST STABILITY; SUBINTERVALS; TIME-VARYING DELAY;

LYAPUNOV FUNCTIONS; STABILITY CRITERIA; TIME VARYING CONTROL SYSTEMS;

LINEAR MATRIX INEQUALITIES;

EID: 84859206009     PISSN: 13494198     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. Y. Abe, M. Konishi and J. Imai, Neural network based diagnosis system for looper height controller of hot strip mills, International Journal of Innovative Computing, Information and Control, vol.3, no.4, pp.919-935, 2007.
2. K. Zou, J. Hu and X. Kong, The structure optimized fuzzy clustering neural network model and its application, International Journal of Innovative Computing, Information and Control, vol.4, no.7, pp.1627-1634, 2008.
3. Z. Wang, H. Gao, J. Cao and X. Liu, On delayed genetic regulatory networks with polytypic uncertainties: Robust stability analysis, IEEE Transactions on Nanobioscience, vol.7, no.2, pp.154-163, 2008.
4. Q. Zhou, S. Xu, B. Chen, H. Li and Y. Chu, Stability analysis of delayed genetic regulatory networks with stochastic disturbances, Physics Letters A, vol.373, pp.3715-3723, 2009.
5. Z. Wang, F. Yang, D. Ho, S. Swift, A. Tucker and X. Liu, Stochastic dynamic modeling of short gene expression time-series data, IEEE Transactions on Nanobioscience, vol.57, no.1, pp.44-55, 2008.
6. G. Wang and J. Cao, Robust exponential stability analysis for stochastic genetic networks with uncertain parameters, Communications in Nonlinear Science and Numerical Simulation, vol.14, no.8, pp.3369-3378, 2009.
7. J. Liu and D. Yue, Asymptotic and robust stability of T-S fuzzy genetic regulatory networks with time-varying delays, International Journal of Robust and Nonlinear Control, vol.21, 2011.
8. H. Li and X. Yang, Asymptotic stability analysis of genetic regulatory networks with time-varying delay, 2010 Chinese Control and Decision Conference, pp.566-571, 2010.
9. H. Bolouri and E. Davidson, Modeling transcriptional regulatory networks, BioEssays, vol.24, no.12, pp.1118-1129, 2002.
10. P. Smolen, D. Baxter and J. Byrne, Mathematical modeling of gene networks, Neuron, vol.26, no.3, pp.567-580, 2000.
11. Y. Sun, G. Feng and J. Cao, Stochastic stability of Markovian switching genetic regulatory networks, Physics Letters A, vol.373, no.18-19, pp.1646-1652, 2009.
12. J. Cao and F. Ren, Exponential stability of discrete-time genetic regulatory networks with delays, IEEE Transactions on Neural Networks, vol.19, no.3, pp.520-523, 2008.
13. J. Liang, J. Lam and Z. Wang, State estimation for Markov-type genetic regulatory networks with delays and uncertain mode transition rates, Physics Letters A, vol.373, no.47, pp.4328-4337, 2009.
14. G. Wei, Z. Wang, J. Lam, K. Fraser, G. Rao and X. Liu, Robust filtering for stochastic genetic regulatory networks with time-varying delay, Mathematical Biosciences, vol.220, no.2, pp.73-80, 2009.
15. T. Gardner, C. Cantor and J. Collins, Construction of a genetic toggle switch in Escherichia coli, Nature, vol.403, no.6767, pp.339-342, 2000.
16. M. Elowitz and S. Leibler, A synthetic oscillatory network of transcriptional regulators, Nature, vol.403, no.6767, pp.335-338, 2000.
17. A. Becskei and L. Serrano, Engineering stability in gene networks by autoregulation, Nature, vol.405, no.6786, pp.590-593, 2000.
18. ∞ control of systems with uncertainty, Auto-matica, vol.41, no.6, pp.999-1007, 2005.
19. D. Yue, E. Tian and Y. Zhang, A piecewise analysis method to stability analysis of linear continuous/discrete systems with time-varying delay, International Journal of Robust and Nonlinear Control, vol.19, no.13, 2009.
20. C. Li, L. Chen and K. Aihara, Stability of genetic networks with SUM regulatory logic: Lur'e system and LMI approach, IEEE Transactions on Circuits and Systems I: Regular Papers, vol.53, no.11, pp.2451-2458, 2006.
21. 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, 2008.
22. H. de Jong, Modeling and simulation of genetic regulatory systems: A literature review, Journal of Computational Biology, vol.9, no.1, pp.67-103, 2002.
23. R. Wang, T. Zhou, Z. Jing and L. Chen, Modelling periodic oscillation of biological systems with multiple time scale networks, Syst. Biol., vol.1, no.1, pp.71-84, 2004.
24. C. Yuh, H. Bolouri and E. Davidson, Genomic cis-regulatory logic: Experimental and computational analysis of a sea urchin gene, Science, vol.279, no.5358, pp.1896-1902, 1998.
25. N. Monk, Oscillatory expression of Hes1, p53, and NF-κB driven by transcriptional time delays, Current Biology, vol.13, no.16, pp.1409-1413, 2003.
26. C. Li, L. Chen and K. Aihara, Synchronization of coupled nonidentical genetic oscillators, Physical Biology, vol.3, pp.37-44, 2006.
27. Q. Han and D. Yue, Absolute stability of Lur'e systems with time-varying delay, Control Theory & Applications, IET, vol.1, no.3, pp.854-859, 2007.
28. D. Yue, E. Tian, Y. Zhang and C. Peng, Delay-distribution-dependent stability and stabilization of T-S fuzzy systems with probabilistic interval delay, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol.39, no.2, pp.503-516, 2009.