zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Robust stability for genetic regulatory networks with linear fractional uncertainties. (English) Zbl 1239.92041
Summary: The asymptotic stability analysis problem for a class of delayed genetic regulatory networks (GRNs) with linear fractional uncertainties and stochastic perturbations is studied. By employing a more effective Lyapunov functional and using a lemma to estimate the derivatives of the Lyapunov functional, some new sufficient conditions for the stability problem of GRNs are derived in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are used to demonstrate the usefulness of the main results and less conservatism of the derived conditions.
92C42Systems biology, networks
34K20Stability theory of functional-differential equations
15A45Miscellaneous inequalities involving matrices
[1]Becskei, A.; Serrano, L.: Engineering stability in gene networks by autoregulation, Nature 405, 590-593 (2000)
[2]Bolouri, H.; Davidson, E. H.: Modeling transcriptional regulatory networks, Bioessays 24, 1118-1129 (2002)
[3]Jong, H.: Modeling and simulation of genetic regulatory systems, a literature review, J comput biol 9, 67-103 (2002)
[4]Elowitz, M. B.; Leibler, S.: A synthetic oscillatory network of transcriptional regulators, Nature 403, 335-338 (2000)
[5]Gardner, T. S.; Cantor, C. R.; Collins, J. J.: Construction of a genetic toggle switch in escherichia coli, Nature 403, 339-342 (2000)
[6]Friedman, N.; Linial, M.; Nachman, I.: Using Bayesian networks to analyze expression data, J comput biol 7, 601-620 (2000)
[7]Hartemink, A. J.; Gifford, D. K.; Jaakkola, T. S.: Bayesian methods for elucidating genetic regulatory networks, IEEE intell syst 17, 37-43 (2002)
[8]Huang, S.: Gene expression profiling genetic regulatory networks and cellular states: an integrating concept for tumorigenesis and drug discovery, J mol med 77, 469-480 (1999)
[9]Kauffman, S. A.: Metabolic stability and epigenesist in randomly constructed genetic nets, J theor biol 22, 437-467 (1969)
[10]Chen, L.; Aihara, K.: Stability of genetic regulatory networks with time delay, IEEE trans circuits syst I 49, 602-608 (2002)
[11]He, Y.; Fu, L.; Zeng, J.: Stability of genetic regulatory networks with interval time-varying delays and stochastic perturbation, Asian J control 13, 625-634 (2011)
[12]Tang, Y.; Wang, Z.; Fang, J.: Parameters identification of unknown delayed genetic regulatory networks by a switching particle swarm optimization algorithm, Expert syst appl 38, 2523-2535 (2011)
[13]Blyuss, K. B.; Gupta, S.: Stability and bifurcations in a model of antigenic variation in malaria, J math biol 58, 923-937 (2009) · Zbl 1204.92045 · doi:10.1007/s00285-008-0204-0
[14]Li, C.; Chen, L.; Aihara, K.: Synchronization of coupled nonidentical genetic oscillators, Phy bio 3, 37-44 (2006)
[15]Li, H.; Wang, C.; Shi, P.: New passivity results for uncertain discrete-time stochastic neural networks with mixed time delays, Neurocomputing 73, 3291-3299 (2010)
[16]Li, H.; Gao, H.; Shi, P.: New passivity analysis for neural networks with discrete and distributed delays, IEEE trans neural netw 21, 1842-1847 (2010)
[17]Li, C.; Chen, L.; Aihara, K.: Stability of genetic networks with sum regulatory logic: lur’s system and LMI approach, IEEE trans circuits syst I 53, 2451-2458 (2006)
[18]Zhou, Q.; Xu, S.; Chen, S. B.: Stability analysis of delayed genetic regulatory networks with stochastic disturbances, Phys lett A 373, 3715-3723 (2009) · Zbl 1233.35197 · doi:10.1016/j.physleta.2009.08.036
[19]F.X. Wu, Stability analysis of genetic regulatory networks with multiple time delays. In: Conf proc IEEE eng med biol soc, 2007, p. 1387 – 1390.
[20]Ren, F.; Cao, J.: Asymptotic and robust stability of genetic regulatory networks with time-varying delays, Neurocomputing 71, 834-842 (2008)
[21]Wang, Z.; Gao, H.; Cao, J.: On delayed genetic regulatory networks with polytopic uncertainties: robost stability analysis, IEEE trans nanbiosci 7, 154-163 (2008)
[22]Tian, T.; Burragea, K.; Burragea, P. M.: Stochastic delay differential equations for genetic regulatory networks, J comput appl 205, 696-707 (2007) · Zbl 1112.92029 · doi:10.1016/j.cam.2006.02.063
[23]Wu, H.; Liao, X.; Guo, S.: Stochastic stability for uncertain genetic regulatory networks with interval time-varying delays, Neurocomputing 72, 3263-3276 (2009)
[24]Li, P.; Lam, J.; Shu, Z.: On the transient and steady-state estimates of interval genetic regulatory networks, IEEE trans syst man cybern B cybern 40, 335-348 (2010)
[25]Balasubramaniam, P.; Rakkiyappan, R.; Krishnasamy, R.: Stochastic stability of Markovian jumping uncertain stochastic genetic regulatory network with interval time varying delays, Math biosci 226, 97-108 (2010) · Zbl 1194.92030 · doi:10.1016/j.mbs.2010.04.002
[26]Chesi, G.; Hung, Y. S.: Stability analysis of uncertain genetic sum regulatory networks, Automatica 44, 2298-2305 (2008) · Zbl 1153.93016 · doi:10.1016/j.automatica.2008.01.030
[27]Chen, B.; Chen, P.: Robust engineered circuit design principles for stochastic biochemical networks with parameter uncertainties and disturbances, IEEE trans biomed circuits syst 2, 114132 (2008)
[28]K. Gu, An integral inequality in the stability problem of time-delay systems. In: 39th IEEE Conference on Decision and Control, Sydney, Australia Dec 2000, p. 2805 – 2810.
[29]Boyd, S.; Ghaoui, L. E.; Feron, E.: Linear matrix inequalities in system and control theory, (1994)
[30]Li, H.: New criteria for synchronization stability of ontinuous complex dynamical networks with non-delayed and delayed coupling, Commun nonlinear sci number simulat 16, 1027-1043 (2011) · Zbl 1221.34198 · doi:10.1016/j.cnsns.2010.05.001
[31]Zhang, Q.; Wei, X.; Xu, J.: Global exponential stability for nonautomous cellular neural networks with delays, Phys lett A 372, 1061-1069 (2008)