Robust exponential stability analysis for stochastic genetic networks with uncertain parameters

Communications in Nonlinear Science and Numerical Simulation

Volumn 14, Issue 8, 2009, Pages 3369-3378

  Wang, Guanjun ^a   Cao, Jinde ^a  

^a SOUTHEAST UNIVERSITY   (China)

Author keywords

02.30.Ks; 05.10.Gg; 87.10.+e; It 's formula; Lyapunov functional; Robust exponential stability in the mean square; Stochastic genetic network; Uncertain parameter

Indexed keywords

LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; STOCHASTIC SYSTEMS; UNCERTAINTY ANALYSIS;

+E; 02.30.; 05.10.; 87.10.; EXPONENTIAL STABILITY IN THE MEAN SQUARES; GG; ITÖ FORMULA; KS; LYAPUNOV FUNCTIONALS; ROBUST EXPONENTIAL STABILITY; ROBUST EXPONENTIAL STABILITY IN THE MEAN SQUARE; STOCHASTIC GENETIC NETWORK; STOCHASTICS; UNCERTAIN PARAMETERS;

STABILITY CRITERIA;

EID: 60849085972     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2009.01.004     Document Type: Article

References (23)

1. Goodwin B.C. Temporal organization in cells (1963), Academic Press, New York
2. Chen T, He H, Church GM. Modeling gene expression with differential equations. In: Proc Pac Symp Biocomputing, vol. 4. 1999. p. 29-40.
3. De Jong H. Modelling and simulation of genetic regulatory systems: a literature review. J Comp Biol 9 (2002) 67-103
4. Chen L., and Aihara K. Stability of genetic regulatory networks with time delay. IEEE Trans CAS-I 49 (2002) 602-608
5. Tian T., Burragea K., Burragea P.M., and Carlettib M. Stochastic delay differential equations for genetic regulatory networks. J Comput Appl 205 (2007) 696-707
6. Li C., Chen L., and Aihara K. Stability of genetic networks with SUM regulatory logic: lure system and LMI approach. IEEE Trans Circuits Syst I 53 (2006) 2451-2458
7. Cao J., and Ren F. Exponential stability of discrete-time genetic regulatory networks with delays. IEEE Trans Neural Netwk 19 (2008) 520-523
8. Chesi G., and Hung Y.S. Stability analysis of uncertain genetic sum regulatory networks. Automatica 44 (2008) 2298-2305
9. Ren F., and Cao J. Robust stability of genetic regulatory networks with interval time-varying delays. Neurocomputing 71 (2008) 834-842
10. Elowitz M.B., Levine A.J., Siggia E.D., and Swain P.S. Stochastic gene expression in a single cell. Science 297 (2002) 1183-1186
11. Paulsson J. Summing up the noise in gene networks. Nature 427 (2004) 415-418
12. Tomioka R., Kimurab H., Kobayashib T.J., and Aihara K. Multivariate analysis of noise in genetic regulatory networks. J Theor Biol 229 (2004) 501-521
13. Raser J.M., and OShea E.K. Noise in gene expression: origins, consequences, and control. Science 309 (2005) 2010-2013
14. Chen L., Wang R., Zhou T., and Aihara K. Noise-induced cooperative behavior in a multicell system. Bioinformatics 21 (2005) 2722-2729
15. Mao X., Koroleva N., and Rodkina A. Robust stability of uncertain stochastic differential delay equations. Syst Contr Lett 35 (1998) 325-336
16. Cao J., and Wang J. Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans Circuit Syst I 52 (2005) 417-426
17. Wang Z., Lauria S., Fang J., and Liu X. Exponential stability of uncertain stochastic neural networks with mixed time-delays. Chaos Solitons Fract 32 (2007) 62-72
18. Li C., and Liao X. Robust stability and robust periodicity of delayed recurrent neural networks with noise disturbance. IEEE Trans Circuit Syst I 53 10 (2006) 2265-2273
19. Sanchez E.N., and Perez J.P. Input-to-state stability (ISS) analysis for dynamics NN. IEEE Trans Circuits Syst I 46 (1999) 1395-1398
20. Boyd S., Ghaoui L.E., Feron E., and Balakrishnan V. Linear matrix inequalities in system and control theory (1994), SIAM, Philadelphia
21. Elwitz M.B., and Leiber S. A synthetic oscillatory network of transcriptional regulator. Nature 403 (2000) 335-338
22. He W., and Cao J. Robust stability of genetic regulatory networks with distributed delay. Cognitive Neurodynam 2 4 (2008) 355-361
23. Xiao M., and Cao J. Genetic oscillation deduced from Hopf bifurcation in a genetic regulatory network with delays. Math Biosci 215 1 (2008) 55-63