Your browser does not support JavaScript!
http://iet.metastore.ingenta.com
1887

access icon free Delay-dependent robust dissipative filtering of stochastic genetic regulatory networks with time-varying delays

© The Institution of Engineering and Technology
Received 13/01/2013, Accepted 01/05/2013, Revised 18/04/2013, Published

This study deals with the problem of delay-dependent dissipative filtering for genetic regulatory networks (GRNs) with norm-bounded parameter uncertainties and time-varying delays. It is assumed that the non-linear function describing the feedback regulation satisfies the sector-bounded condition. Improved delay-dependent stochastic stability and filter design method for stochastic GRNs are obtained by applying the delay fractioning technique, Jensen inequalities and introducing some proper slack matrix variables. The conservatism caused by either model transformation or bounding techniques is reduced. Sufficient conditions of the robust stability and filtering problems are proposed, respectively. The filter, which can guarantee the resulting error system to be asymptotically stable in the mean-square sense and satisfy a prescribed performance level for all delays no larger than a given upper bound, are constructed. A numerical example is provided to demonstrate effectiveness of the proposed results in this study.

Inspec keywords: biology; information filtering; delays; time-varying systems; matrix algebra; stochastic processes; feedback; mean square error methods

Other keywords: nonlinear function; GRN; delay dependent robust dissipative filtering; delay dependent stochastic stability; time varying delays; Jensen inequalities; norm bounded parameter uncertainties; filtering problems; mean-square sense; slack matrix variables; error system; filter design method; stochastic genetic regulatory networks; robust stability; bounding techniques; delay fractioning technique; feedback regulation; sector bounded condition

Subjects: Linear algebra (numerical analysis); Interpolation and function approximation (numerical analysis); Biology and medical computing; Information retrieval techniques; Other topics in statistics

References

    1. 1)
      • 21. Yu, W., Lv, J., Chen, G., et al: ‘Estimating uncertain delayed genetic regulatory networks: an adaptive filtering approach’, IEEE Trans. Autom. Control, 2009, 54, (4), pp. 892–897 (doi: 10.1109/TAC.2008.2010972).
    2. 2)
      • 33. Li, C., Chen, L., Aihara, K.: ‘Stochastic synchronization of genetic oscillator networks’, BMC Syst. Biol., 2007, 1, (6), pp. 1–11.
    3. 3)
      • 4. Wang, Z., Lam, J., Wei, G., et al: ‘Filtering for nonlinear genetic regulatory networks with stochastic disturbances’, IEEE Trans. Autom. Control, 2008, 53, (10), pp. 2448–2457 (doi: 10.1109/TAC.2008.2007862).
    4. 4)
      • 5. Wei, G., Wang, Z., Lam, J., et al: ‘Robust filtering for stochastic genetic regulatory networks with time-varying delay’, Math. Biosci., 2009, 220, (2), pp. 73–80 (doi: 10.1016/j.mbs.2009.04.002).
    5. 5)
      • 14. Sakthivel, R., Raja, R., Marshal Anthoni, S.: ‘Asymptotic stability of delayed stochastic genetic regulatory networks with impulses’, Phys. Scr., 2010, 82, (5), pp. 1–7, Article no. 055009 (doi: 10.1088/0031-8949/82/05/055009).
    6. 6)
      • 30. Zhang, D., Yu, L.: ‘H∞ passivity analysis for stochastic Markovian switching genetic regulatory networks with time-varying delays’, Commun. Nonlinear Sci. Numer. Simul., 2011, 16, (8), pp. 2985–2992 (doi: 10.1016/j.cnsns.2010.12.006).
    7. 7)
      • 31. Lu, C.Y., Su, Y.M., Chang, H.C., Huang, H.C.: ‘Delay-dependent robust passivity analysis for uncertain genetic regulatory networks with interval time-varying delays’, Proc. 2011 Eighth Asian Control Conf., 2011, pp. 193–198.
    8. 8)
      • 19. Wang, Z., Yang, F., Ho, D.W. C., et al: ‘Stochastic dynamic modeling of short gene expression time series data’, IEEE Trans. NanoBiosci., 2008, 7, (1), pp. 44–55 (doi: 10.1109/TNB.2008.2000149).
    9. 9)
      • 13. Pal, R., Bhattacharya, S.: ‘Transient dynamics of reduced-order models of genetic regulatory networks’, IEEE/ACM Trans. Comput. Biol. Bioinf., 2012, 9, (4), pp. 1230–1244 (doi: 10.1109/TCBB.2012.37).
    10. 10)
      • 12. Chesi, G.: ‘On the steady States of uncertain genetic regulatory networks’, IEEE Trans. Syst. Man Cybern. A, Syst. Humans, 2012, 42, (4), pp. 1020–1024 (doi: 10.1109/TSMCA.2011.2178829).
    11. 11)
      • 24. Willems, J.C.: ‘Dissipative dynamical systems, Part II: linear systems with quadratic supply rates’, Arch. Ration. Mech. Anal., 1972, 45, (5), pp. 352–393 (doi: 10.1007/BF00276494).
    12. 12)
      • 29. Mathiyalagan, K., Sakthivel, R., Marshal Anthoni, S.: ‘New robust passivity criteria for discrete-time genetic regulatory networks with Markovian jumping parameters’, Can. J. Phys., 2012, 90, pp. 107–118 (doi: 10.1139/p11-147).
    13. 13)
      • 6. Wang, Y., Wang, Z., Wang Liang, J.: ‘On robust stability of stochastic genetic regulatory networks with time delays: a delay fractioning approach’, IEEE Trans. Syst. Man Cybern. B, Cybern., 2010, 40, (3), 729–740 (doi: 10.1109/TSMCB.2009.2026059).
    14. 14)
      • 32. Li, Y.J., Duan, G.R.: ‘Robust dissipative control for T–S fuzzy systems’, J. Syst. Eng. Electron., 2009, 20, (3), pp. 598–606.
    15. 15)
      • 7. Mousavi, S.M., Majd, V.J.: ‘Robust filtering of extended stochastic genetic regulatory networks with parameter uncertainties, disturbances, and time-varying delays’, Neurocomputing, 2011, 74, (12–13), pp. 2123–2134 (doi: 10.1016/j.neucom.2011.01.018).
    16. 16)
      • 26. Feng, Z.G., Lam, J.: ‘Robust reliable dissipative filtering for discrete delay singular systems’, Signal Process., 2012, 92, (1), pp. 3010–2025 (doi: 10.1016/j.sigpro.2012.06.003).
    17. 17)
      • 27. Mathiyalagan, K., Sakthivel, R.: ‘Robust stabilization and H∞ control for discretetime stochastic genetic regulatory networks with time delays’, Can. J. Phys., 2012, 90, pp. 939–953 (doi: 10.1139/p2012-088).
    18. 18)
      • 25. Duan, G.R., Lv, L.L., Wu, A.G.: ‘Robust dissipative filtering for continuous-time polytopic uncertain neutral systems’, J. Syst. Eng. Electron., 2009, 29, (9), pp. 1518–1523.
    19. 19)
      • 10. Li, F.F., Sun, J.T.: ‘Controllability and optimal control of a temporal Boolean network’, Neural Netw., 2012, 34, pp. 10–17 (doi: 10.1016/j.neunet.2012.06.002).
    20. 20)
      • 18. Chen, T., He, H., Church, G.: ‘Modeling gene expression with differential equations’. Proc. Pacific Symp. Biocomputing, 1999, 4, pp. 29–40.
    21. 21)
      • 23. Willems, J.C.: ‘Dissipative dynamical systems, Part I: general theory’, Arch. Ration. Mech. Anal., 1972, 45, (5), pp. 321–351 (doi: 10.1007/BF00276493).
    22. 22)
      • 11. Tian, L.P., Wang, J.X., Wu, F.X.: ‘Robust and global delay-dependent stability for genetic regulatory networks with parameter uncertainties’, IEEE Trans. Nanobiosci., 2012, 11, (3), pp. 251–258 (doi: 10.1109/TNB.2012.2214231).
    23. 23)
      • 28. Liu, A.D., Yu, L., Zhang, W.A., Chen, B.: ‘H∞ filtering for discrete-time genetic regulatory networks with random delays’, Math. Biosci., 2012, 239, (1), pp. 97–105 (doi: 10.1016/j.mbs.2012.05.002).
    24. 24)
      • 15. Mathiyalagan, K., Sakthivel, R., Marshal Anthoni, S.: ‘New robust passivity criteria for stochastic fuzzy BAM neural networks with time-varying delays’, Commun. Nonlinear Sci. Numer. Simul., 2012, 17, (3), pp. 1392–1407 (doi: 10.1016/j.cnsns.2011.07.032).
    25. 25)
      • 17. Huang, S.: ‘Gene expression profiling, genetic networks, and cellular states: An integrating concept for tumorigenesis and drug discovery’, J. Mol. Med., 1999, 77, (6), pp. 469–480 (doi: 10.1007/s001099900023).
    26. 26)
      • 1. Pease, A., Solas, D., Sullivan, E., et al: ‘Light-generated oligonucleotide arrays for rapid DNA sequence analysis’, Proc. Natl. Acad. Sci. USA, 1994, 91, pp. 5022–5026 (doi: 10.1073/pnas.91.11.5022).
    27. 27)
      • 22. Liang, J., Lam, J.: ‘Robust state estimation for stochastic genetic regulatory networks’, Int. J. Syst. Sci., 2010, 41, (1), pp. 47–63 (doi: 10.1080/00207720903141434).
    28. 28)
      • 8. Wu, F.X.: ‘Delay-independent stability of genetic regulatory networks’, IEEE Trans. Neural Netw., 2011, 22, (11), pp. 1685–1693 (doi: 10.1109/TNN.2011.2165556).
    29. 29)
      • 2. Gerstein, M.B., Kundaje, A., Hariharan, M., et al: ‘Architecture of the human regulatory network derived from ENCODE data’, Nature, 2012, 489, (7474), pp. 91–100 (doi: 10.1038/nature11245).
    30. 30)
      • 9. Wang, W.Q., Zhong, S.M., Liu, F.: ‘Robust filtering of uncertain stochastic genetic regulatory networks with time-varying delays’, Chaos Solitons Fractals, 2012, 45, (7), pp. 915–929 (doi: 10.1016/j.chaos.2012.03.006).
    31. 31)
      • 3. Elowitz, M.B., Leibler, S.: ‘A synthetic oscillatory network of transcriptional regulators’, Nature, 2000, 403, (6767), pp. 335–338 (doi: 10.1038/35002125).
    32. 32)
      • 20. 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., 2010, 40, (2), pp. 336–349 (doi: 10.1109/TSMCB.2009.2022402).
    33. 33)
      • 16. Thomas, R.: ‘Boolean formalization of genetic control circuits’, J. Theor. Biol., 1973, 42, (3), pp. 563–585 (doi: 10.1016/0022-5193(73)90247-6).
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2013.0040
Loading

Related content

content/journals/10.1049/iet-cta.2013.0040
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
Print this page
This is a required field
Please enter a valid email address