Robust stability of stochastic genetic network with Markovian jumping parameters

Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering

Volumn 223, Issue 6, 2009, Pages 797-807

  Wang, G ^a   Cao, J ^a   Liang, J ^a  

^a SOUTHEAST UNIVERSITY   (China)

Author keywords

It 's formula; Linear matrix inequality; Lyapunov functional; Markovian jumping parameter; Robust stability in the mean square; Stochastic genetic networks

Indexed keywords

CONTINUOUS TIME; GENETIC MODELS; GENETIC NETWORKS; GENETIC SYSTEMS; ILLUSTRATIVE EXAMPLES; JUMPING PARAMETERS; LMI-CONDITION; LYAPUNOV FUNCTIONAL; LYAPUNOV FUNCTIONALS; MARKOVIAN; MARKOVIAN JUMPING PARAMETER; MARKOVIAN JUMPING PARAMETERS; PARAMETER UNCERTAINTY; ROBUST EXPONENTIAL STABILITY; ROBUST STABILITY; ROBUST STABILITY IN THE MEAN SQUARE; STABILITY PROBLEM; STOCHASTIC ANALYSIS; STOCHASTIC DISTURBANCES; STOCHASTIC GENETIC NETWORKS; UNCERTAIN PARAMETERS;

DELAY CONTROL SYSTEMS; FUZZY CONTROL; LINEAR CONTROL SYSTEMS; LINEAR MATRIX INEQUALITIES; MARKOV PROCESSES; ROBUSTNESS (CONTROL SYSTEMS); SYSTEM STABILITY; UNCERTAIN SYSTEMS; UNCERTAINTY ANALYSIS;

STABILITY CRITERIA;

EID: 70349226976     PISSN: 09596518     EISSN: None     Source Type: Journal    
DOI: 10.1243/09596518JSCE772     Document Type: Article

References (17)

1. Chen, T., He, H. L., and Church, G. M. Modeling gene expression with differential equations. In Proceedings of the 4th Pacific Symposium on Biocomputing, Hawaii, USA, 1999, pp. 29-40 (World Scientific, Hawaii).
2. de Jong, H. Modelling and simulation of genetic regulatory systems: a literature review. J. Comput. Biol., 2002, 9, 67-103.
3. Elwitz, M. B. and Leiber, S. A synthetic oscillatory network of transcriptional regulator. Nature, 2000, 403, 335-338.
4. Tian, T., Burragea, K., Burragea, P. M., and Carlettib, M. Stochastic delay differential equations for genetic regulatory networks. J. Comput. Appl. Math., 2007, 205, 696-707.
5. Elowitz, M. B., Levine, A. J., Siggia, E. D., and Swain, P. S. Stochastic gene expression in a single cell. Science, 2002, 297, 1183-1186.
6. Li, C., Chen, L., and Aihara, K. Stochastic stability of genetic networks with disturbance attenuation. IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., 2007, 54, 892-896.
7. Paulsson, J. Summing up the noise in gene networks. Nature, 2004, 427, 415-418.
8. Tomioka, R., Kimurab, H., Kobayashib, T. J., and Aihara, K. Multivariate analysis of noise in genetic regulatory networks. J. Theor. Biol., 2004, 229, 501-521.
9. Chen, L. and Aihara, K. Stability of genetic regulatory networks with time delay. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 2002, 49, 602-608.
10. 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, Fundam. Theory Appl., 2006, 53, 2451-2458.
11. Cao, J. and Ren, F. Exponential stability of discrete-time genetic regulatory networks with delays. IEEE Trans. Neural Net., 2008, 19, 520-523.
12. Cao, J. and Wang, J. Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 2005, 52, 417-426. (Pubitemid 40319475)
13. Mao, X., Koroleva, N., and Rodkina, A. Robust stability of uncertain stochastic differential delay equations. Syst. Control Lett, 1998, 35, 325-336.
14. Wang, Z., Lauria, S., Fang, J., and Liu, X. Exponential stability of uncertain stochastic neural networks with mixed time-delays. Chaos Solitons Fractals, 2007, 32, 62-72. (Pubitemid 44374960)
15. Chesi, G. and Hung, Y. S. Stability analysis of uncertain genetic sum regulatory networks. Automatica, 2008, 44, 2298-2305.
16. He, W. and Cao, J. Robust stability of genetic regulatory networks with distributed delay. Cog. Neurodyn., 2008, 2(4), 355-361.
17. Ren, F. and Cao, J. Robust stability of genetic regulatory networks with interval time-varying delays. Neurocomputing, 2008, 71, 834-842. (Pubitemid 351168429)