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Original Articles

Partial stability and stabilisation of Boolean networks

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Pages 2119-2127 | Received 18 Jan 2014, Accepted 03 Oct 2014, Published online: 31 Oct 2014

References

  • Aldana, M. (2003). Boolean dynamics of networks with scale-free topology. Physica D: Nonlinear Phenomena 185(1), 45–66.
  • Awad, E., & Culick, F. (1986). On the existence and stability of limit cycles for longitudinal acoustic modes in a combustion chamber. Combustion Science and Technology 46(3–6), 195–222.
  • Chen, H., Liu, Y., & Lu, J. (2013). Synchronization criteria for two Boolean networks based on logical control. International Journal of Bifurcation and Chaos 23(1), 1350178.
  • Cheng, D., Li, Z., & Qi, H. (2010). Realization of Boolean control networks. Automatica 46(1), 62–69.
  • Cheng, D., & Qi, H. (2009). Controllability and observability of Boolean control networks. Automatica 45(7), 1659–1667.
  • Cheng, D., & Qi, H. (2010). A linear representation of dynamics of Boolean networks. IEEE Transactions on Automatic Control 55(10), 2251–2258.
  • Cheng, D., Qi, H., & Li, Z. (2011). Analysis and control of Boolean networks: A semi-tensor product approach. New York, NY: Springer.
  • Cheng, D., Qi, H., Li, Z., & Liu, J. (2011). Stability and stabilization of Boolean networks. International Journal of Robust and Nonlinear Control 21(2), 134–156.
  • Dong, H., Wang, Z., Li, Z., & Gao, H. (2011). Distributed H∞ filtering for a class of Markovian jump nonlinear time-delay systems over lossy sensor networks. IEEE Transactions on Industrial Electronics 60(10), 4665–4672.
  • Hale, J.K., & Lunel, S.V. (2003). Stability and control of feedback systems with time delays. International Journal of Systems Science 34(8–9), 497–504.
  • Heidel, J., Maloney, J., Farrow, C., & Rogers, J. (2003). Finding cycles in synchronous Boolean networks with applications to biochemical systems. International Journal of Bifurcation and Chaos 13(03), 535–552.
  • Kauffman, S.A. (1969). Metabolic stability and epigenesis in randomly constructed genetic nets. Journal of Theoretical Biology 22(3), 437–467.
  • Laschov, D., & Margaliot, M. (2011). A maximum principle for single-input Boolean control networks. IEEE Transactions on Automatic Control 56(4), 913–917.
  • Laschov, D., & Margaliot, M. (2012). Controllability of Boolean control networks via the Perron–Frobenius theory. Automatica 48(6), 1218–1223.
  • Li, F., & Sun, J. (2012). Stability and stabilization of Boolean networks with impulsive effects. Systems & Control Letters 61(1), 1–5.
  • Li, H., & Wang, Y. (2013). Consistent stabilizability of switched Boolean networks. Neural Networks 46, 183–189.
  • Li, R., & Chu, T. (2012). Complete synchronization of Boolean networks. IEEE Transactions on Neural Networks and Learning Systems 23(5), 840–846.
  • Li, R., Yang, M., & Chu, T. (2013). State feedback stabilization for Boolean control networks. IEEE Transactions on Automatic Control 58(7), 1853–1857.
  • Liu, Y., Chen, H., & Lu, J. (2014). Data-based controllability analysis of discrete-time linear time-delay systems. International Journal of Systems Science 45(11), 2411–2417.
  • Liu, Y., Chen, H., & Wu, B. (2014). Controllability of Boolean control networks with impulsive effects and forbidden states. Mathematical Methods in the Applied Sciences 37(1), 1–9.
  • Liu, Y., Lu, J., & Wu, B. (2014). Some necessary and sufficient conditions for the output controllability of temporal Boolean control networks. ESAIM: Control, Optimisation and Calculus of Variations 20(1), 158–173.
  • Lum, K.Y., Bernstein, D.S., & Coppola, V.T. (1995). Global stabilization of the spinning top with mass imbalance. Dynamics and Stability of Systems 10(4), 339–365.
  • Robert, F. (1986). Discrete iterations: A metric study. (J. Rokne, Trans.). Berlin: Springer.
  • Rouche, N., Habets, P., Laloy, M., & Ljapunov, A.M. (1977). Stability theory by Liapunov's direct method. New York: Springer.
  • Vorotnikov, V.I. (1998). Partial stability and control. New York, NY: Springer.
  • Wang, Z., Ding, D., Dong, H., Shen, B., & Gao, H. (2013). Finite-horizon H∞ filtering with missing measurements and quantization effects. IEEE Transactions on Automatic Control 58(7), 1707–1718.
  • Wang, Z., Ding, D., Dong, H., & Shu, H. (2013). H∞ consensus control for multi-agent systems with missing measurements: The finite-horizon case. Systems & Control Letters 62(10), 827–836.
  • Wu, Z., Shi, P., Su, H., & Chu, J. (2012). Delay-dependent stability analysis for discrete-time singular Markovian jump systems with time-varying delay. International Journal of Systems Science 43(11), 2095–2106.
  • Xia, Y., Liu, G.P., Shi, P., Rees, D., & Thomas, E. (2007). New stability and stabilization conditions for systems with time-delay. International Journal of Systems Science 38(1), 17–24.
  • Zhang, Y., Feng, G., & Sun, J. (2013). Stability of impulsive piecewise linear systems. International Journal of Systems Science 44(1), 139–150.
  • Zhao, Y., & Cheng, D. (2013). On controllability and stabilizability of probabilistic Boolean control networks. Science China Information Sciences 57(1), 1–14.

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