Design of delay-range-dependent robust controller for uncertain genetic regulatory networks with interval time-varying delays

This paper investigates the problem of robust stabilization for genetic regulatory networks with interval time-varying delays, which are subject to norm-bounded time-varying parameter uncertainties. The time delays including lower and upper bounds of delay are assumed to appear in both the mRNA and protein. The regulatory functions are assumed to be globally Lipschitz continuous. The resulting delay-range-dependent robust controller with interval range is designed in terms of improved bounding technique. A sufficient condition for the solvability of the problem is obtained via a linear matrix inequality (LMI). When this LMI is feasible, an explicit expression of a desired state feedback controller is also given. The theory developed in this paper is demonstrated by two numerical examples.

[1]  Chien-Yu Lu,et al.  On robust stabilization of uncertain stochastic time-delay systems - an LMI-based approach , 2005, J. Frankl. Inst..

[2]  Ping Li,et al.  Feedback control of the genetic networks with time delay , 2004, Fifth World Congress on Intelligent Control and Automation (IEEE Cat. No.04EX788).

[3]  J. Collins,et al.  Construction of a genetic toggle switch in Escherichia coli , 2000, Nature.

[4]  S. Mangan,et al.  Article number: 2005.0006 , 2022 .

[5]  Chien-Yu Lu,et al.  A Delay-Dependent Approach to Passivity Analysis for Uncertain Neural Networks with Time-varying Delay , 2008, Neural Processing Letters.

[6]  M. Elowitz,et al.  A synthetic oscillatory network of transcriptional regulators , 2000, Nature.

[7]  D. A. Baxter,et al.  A reduced model clarifies the role of feedback loops and time delays in the Drosophila circadian oscillator. , 2002, Biophysical journal.

[8]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[9]  Kazuyuki Aihara,et al.  Stability of Genetic Networks With SUM Regulatory Logic: Lur'e System and LMI Approach , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[10]  Jinde Cao,et al.  On Delayed Genetic Regulatory Networks With Polytopic Uncertainties: Robust Stability Analysis , 2008, IEEE Transactions on NanoBioscience.

[11]  Kazuyuki Aihara,et al.  Modeling genetic switches with positive feedback loops. , 2003, Journal of theoretical biology.

[12]  Jinde Cao,et al.  Asymptotic and robust stability of genetic regulatory networks with time-varying delays , 2008, Neurocomputing.

[13]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[14]  Ting Chen,et al.  Modeling Gene Expression with Differential Equations , 1998, Pacific Symposium on Biocomputing.

[15]  N. Monk.  Oscillatory Expression of Hes1, p53, and NF-κB Driven by Transcriptional Time Delays , 2003, Current Biology.

[16]  Farren J. Isaacs,et al.  Computational studies of gene regulatory networks: in numero molecular biology , 2001, Nature Reviews Genetics.

[17]  D. Volfson,et al.  Delay-induced stochastic oscillations in gene regulation. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[18]  Jinde Cao,et al.  Robust State Estimation for Uncertain Neural Networks With Time-Varying Delay , 2008, IEEE Transactions on Neural Networks.

[19]  Cao Jin-de.  Robust State Estimation for Uncertain Neural Networks , 2008 .

[20]  K. Burrage,et al.  Stochastic delay differential equations for genetic regulatory networks , 2007 .

[21]  A. S. Carstea,et al.  On the dynamics of a gene regulatory network , 2006 .

[22]  E. Davidson,et al.  Genomic cis-regulatory logic: experimental and computational analysis of a sea urchin gene. , 1998, Science.

[23]  Wei Zhang,et al.  A note on the robust stability of genetic regulatory networks with time-varying delays , 2008, 2008 IEEE Conference on Cybernetics and Intelligent Systems.

[24]  Vladimir A. Yakubovich,et al.  Linear Matrix Inequalities in System and Control Theory (S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan) , 1995, SIAM Rev..

[25]  Sui Huang.  Gene expression profiling, genetic networks, and cellular states: an integrating concept for tumorigenesis and drug discovery , 1999, Journal of Molecular Medicine.

[26]  L. Serrano,et al.  Engineering stability in gene networks by autoregulation , 2000, Nature.

[27]  K. Aihara,et al.  Stability of genetic regulatory networks with time delay , 2002 .

[28]  H. McAdams,et al.  Circuit simulation of genetic networks. , 1995, Science.

[29]  C. Pao,et al.  Models of genetic control by repression with time delays and spatial effects , 1984, Journal of mathematical biology.