H∞ filtering for discrete-time genetic regulatory networks with random delays.

The H(∞) filtering problem is investigated in this paper for a class of discrete-time genetic regulatory networks (GRNs) with random delays. The addressed filtering problem is to estimate the concentrations of mRNA and protein, and the filtering error system is modeled as a Markovian switched system. By using a properly constructed Lyapunov function, a sufficient condition is derived in terms of linear matrix inequalities (LMIs), which can guarantee stochastic stabilization of the filtering error system. Then, an optimization problem with LMIs constraints is established to design an H(∞) filter which ensures an optimal H(∞) disturbance attenuation level. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed results.

[1]  James Lam,et al.  Filtering for Nonlinear Genetic Regulatory Networks With Stochastic Disturbances , 2008, IEEE Transactions on Automatic Control.

[2]  E. Dougherty,et al.  MODELING GENETIC REGULATORY NETWORKS: CONTINUOUS OR DISCRETE? , 2006 .

[3]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[4]  Bor-Sen Chen,et al.  Robust $H_{\infty}$-Stabilization Design in Gene Networks Under Stochastic Molecular Noises: Fuzzy-Interpolation Approach , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[5]  Fuwen Yang,et al.  Robust H/sub /spl infin// filtering for stochastic time-delay systems with missing measurements , 2006, IEEE Transactions on Signal Processing.

[6]  Bor-Sen Chen,et al.  Robust filtering circuit design for stochastic gene networks under intrinsic and extrinsic molecular noises. , 2008, Mathematical biosciences.

[7]  Pin-Lin Liu.  Robust Stability for Uncertain Genetic Regulatory Networks with Interval Time-varying Delays , 2012 .

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

[9]  Zidong Wang,et al.  Robust filtering for gene expression time series data with variance constraints , 2007, Int. J. Comput. Math..

[10]  Zidong Wang,et al.  Robust filtering for stochastic genetic regulatory networks with time-varying delay. , 2009, Mathematical biosciences.

[11]  Julian Lewis.  Autoinhibition with Transcriptional Delay A Simple Mechanism for the Zebrafish Somitogenesis Oscillator , 2003, Current Biology.

[12]  Pll Siinksen,et al.  Control , 1999 .

[13]  H. Hirata,et al.  Oscillatory Expression of the bHLH Factor Hes1 Regulated by a Negative Feedback Loop , 2002, Science.

[14]  Wei Zhang,et al.  Robust stability for uncertain genetic regulatory networks with interval time-varying delays , 2010, Inf. Sci..

[15]  Zengrong Liu,et al.  Periodic oscillation in delayed gene networks with SUM regulatory logic and small perturbations. , 2009, Mathematical biosciences.

[16]  Xiaoming Chen,et al.  H∞ filtering with stochastic sampling , 2010, Signal Process..

[17]  Jinde Cao,et al.  Exponential Stability of Discrete-Time Genetic Regulatory Networks With Delays , 2008, IEEE Transactions on Neural Networks.

[18]  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.

[19]  R. Lima,et al.  Dynamical complexity of discrete-time regulatory networks , 2005, math/0509141.

[20]  R. Coutinho,et al.  Discrete time piecewise affine models of genetic regulatory networks , 2005, Journal of mathematical biology.

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

[22]  Yuanqing Xia,et al.  Parameter-dependent robust H∞ filtering for uncertain discrete-time systems , 2009, Autom..

[23]  C. Rao,et al.  Control, exploitation and tolerance of intracellular noise , 2002, Nature.

[24]  James Lam,et al.  Robust state estimation for stochastic genetic regulatory networks , 2010, Int. J. Syst. Sci..

[25]  Wen-an Zhang,et al.  Hinfinity filtering of network-based systems with random delay , 2009, Signal Process..

[26]  Jinde Cao,et al.  Robust stability of Markovian jumping genetic regulatory networks with disturbance attenuation , 2011 .

[27]  Zidong Wang,et al.  An Extended Kalman Filtering Approach to Modeling Nonlinear Dynamic Gene Regulatory Networks via Short Gene Expression Time Series , 2009, TCBB.

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

[29]  Fei Liu,et al.  Finite-time filtering for non-linear stochastic systems with partially known transition jump rates , 2010 .

[30]  Daniel W. C. Ho,et al.  Robust ${{\cal H}}_{\infty}$ Filtering for Markovian Jump Systems With Randomly Occurring Nonlinearities and Sensor Saturation: The Finite-Horizon Case , 2011, IEEE Transactions on Signal Processing.

[31]  Yeung Sam Hung,et al.  Stability analysis of uncertain genetic sum regulatory networks , 2008, Autom..

[32]  J. Geromel,et al.  A new discrete-time robust stability condition , 1999 .

[33]  Zidong Wang,et al.  An Extended Kalman Filtering Approach to Modeling Nonlinear Dynamic Gene Regulatory Networks via Short Gene Expression Time Series , 2009, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[34]  James Lam,et al.  On robust stabilization of Markovian jump systems with uncertain switching probabilities , 2005, Autom..

[35]  M. C. D. Oliveiraa,et al.  A new discrete-time robust stability condition ( , 1999 .

[36]  Wen-an Zhang,et al.  H∞ Filtering for Markovian Switching Genetic Regulatory Networks with Time-Delays and Stochastic Disturbances , 2011, Circuits Syst. Signal Process..

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

[38]  Baotong Cui,et al.  Mean square exponential and robust stability of stochastic discrete-time genetic regulatory networks with uncertainties , 2010, Cognitive Neurodynamics.