184
Views
9
CrossRef citations to date
0
Altmetric
Original Articles

Stabilisation of stochastic coupled systems via feedback control based on discrete-time state observations

, &
Pages 2850-2859 | Received 11 Oct 2016, Accepted 13 Jun 2017, Published online: 04 Jul 2017

References

  • Aghajani, A., Jalilian, Y., & Roomi, V. (2011). Oscillation theorems for the generalized Lienard system. Mathmetical and Computer Modelling, 9–10, 2471–2478. doi:10.1016/j.mcm.2011.06.004
  • Arik, S. (2016). Dynamical analysis of uncertain neural networks with multiple time delays. International Journal of Systems Science, 47, 730–739. doi:10.1080/00207721.2014.902158
  • Dorfler, F., & Bullo, F. (2014). Synchronization in complex networks of phase oscillators: A survey. Automatica, 6, 1539–1564. doi:10.1016/j.automatica.2014.04.012
  • Deng, H., & Krstic, M. (1997). Stochastic nonlinear stabilization .2. Inverse optimality. Systems & Control Letters, 3, 151–159. doi:10.1016/S0167-6911(97)00067-4
  • Hu, X.X., Wu, L.G., Hu, C.H., Wang, Z.Q., & Gao, H.J. (2014). Dynamic output feedback control of a flexible air-breathing hypersonic vehicle via T-S fuzzy approach. International Journal of Systems Science, 45, 1740–1756. doi:10.1080/00207721.2012.749547
  • Jin, X.L., & Huang, Z.L. (2010). Nonstationary probability densities of strongly nonlinear single-degree-of-freedom oscillators with time delay. Nonlinear Dynamics, 59, 195–206. doi:10.1007/s11071-009-9532-x
  • Kolmanovskii V.B., & Myshkis A.D. (1999). Introduction to the theory and applications of functional differential equations. Dordrecht: Kluwer Academic.
  • Li, F.B., Shi, P., Lim, C.C., & Wu, L.G. (2016). Fault detection filtering for nonhomogeneous Markovian jump systems via fuzzy approach. IEEE Transactions on Fuzzy Systems, 99, 1. doi:10.1109/TFUZZ.2016.2641022
  • Li, M.Y., & Shuai, Z.S. (2010). Global-stability problem for coupled systems of differential equations on networks. Journal of Differential Equations, 1, 1–20. doi:10.1016/j.jde.2009.09.003
  • Li, W.X., Song, H.H., Qu, Y.B., & Wang, K. (2013). Global exponential stability for stochastic coupled systems on networks with Markovian switching. Systems & Control Letters, 6, 468–474. doi:10.1016/j.sysconle.2013.03.001
  • Li, W.X., Su, H., & Wang, K. (2011). Global stability analysis for stochastic coupled systems on networks. Automatica, 1, 215–220. doi:10.1016/j.automatica.2010.10.041
  • Li, R.S., Zhao, Y., Jiang, R., & Wang, H.Q. (2016). Some remarks on chaos of a coupled lattice system related with the Belusov-Zhabotinskii reaction. Journal of Mathematical Chemistry, 4, 849–853. doi:10.1007/s10910-016-0616-9
  • Lu, J.Q., Ho, D.W. C., & Wang, Z.D. (2009). Pinning stabilization of linearly coupled stochastic neural networks via minimum number of controllers. IEEE Transactions on Neural Networks, 10, 1617–1629. doi:10.1109/TNN.2009.2027810
  • Lu, J.G., & Chen, G.R. (2009). Global asymptotical synchronization of chaotic neural networks by output feedback impulsive control: An LMI approach. Chaos Solitons Fractals, 5, 2293–2300. doi:10.1016/j.chaos.2008.09.024
  • Li, F.B., Wu, L.G., Shi, P., & Lim, C.C. (2015). State estimation and sliding mode control for semi-Markovian jump systems with mismatched uncertainties. Automatica, 51, 385–393. doi:10.1016/j.automatica.2014.10.065
  • Lian, J., Feng, Z., & Shi, P. (2011). Observer design for switched recurrent neural networks: An average dwell time approach. IEEE Transactions on Neural Networks, 22(10), 1547–1556. doi:10.1109/TNN.2011.2162111
  • Li, W.X., Yang, H.W., Wen, L., & Wang, K. (2014). Global exponential stability for coupled retarded systems on networks: A graph-theoretic approach. Communications in Nonlinear Science and Numerical Simulation, 6, 1651–1660. doi:10.1016/j.cnsns.2013.09.039
  • Mathiyalagan, K., Park, J.H., & Sakthivel, R. (2015). Synchronization for delayed memristive BAM neural networks using impulsive control with random nonlinearities. Applied Mathematics and Computation, 259, 967–979. doi:10.1016/j.amc.2015.03.022
  • Mao, X.R. (2013). Stabilization of continuous-time hybrid stochastic differential equations by discrete-time feedback control. Automatics, 12, 3677–3681. doi:10.1016/j.automatica.2013.09.005
  • Mao, X.R., Lam, J., & Huang, L.R. (2008). Stabilisation of hybrid stochastic differential equations by delay feedback control. Systems & Control Letters, 11, 927–935. doi:10.1016/j.sysconle.2008.05.002
  • Mao, X.R., Liu, W., Hu, L.J., Luo, Q., & Lu, J.Q. (2014). Stabilization of hybrid stochastic differential equations by feedback control based on discrete-time state observations. Systems & Control Letters,, 73, 88–95. doi:10.1016/j.sysconle.2014.08.011
  • Nabiha, T., & Samira, K. (2015). Design of robust self-tuning control schemes for stochastic systems described by input-output mathematical models. International Journal of Innovative Computing, Information and Control, 11(3), 1101–1112.
  • Panaggio, M.J., & Abrams, D.M. (2015). Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators. Nonlinearity, 28, R67–R87. doi:10.1088/0951-7715/28/3/R67
  • Su, H., Li, W.X., & Wang, K. (2012). Global stability analysis of discrete-time coupled systems on networks and its applications. Chaos, 3, 033135. doi:10.1063/1.4748851
  • Shi, P., Li, F.B., Wu, L.G., & Lim, C.C. (2016). Neural network-based passive filtering for delayed neutral-type semi-markovian jump systems. IEEE Transactions on Neural Networks and Learning Systems, 99, 1–14. doi:10.1109/TNNLS.2016.2573853
  • Su, H., Qu, Y.B., Gao, S., Song, H.H., & Wang, K. (2012). A model of feedback control system on network and its stability analysis. Communications in Nonlinear Science and Numerical Simulation, 7, 1822–1831. doi:10.1016/j.cnsns.2012.10.018
  • Su, X.J., Wu, L.G., Shi, P., & Song, Y.D. (2014). A novel approach to output feedback control of fuzzy stochastic systems. Automatica, 12, 3268–3275. doi:10.1016/j.automatica.2014.10.053
  • Song, H.H., Chen, D.D., & Li, W.X. (2016). Graph-theoretic approach to exponential synchronization of stochastic reaction-diffusion Cohen-Grossberg neural networks with time-varying delays. Neurocomputing, 179–187. doi:10.1016/j.neucom.2015.11.036
  • Sun, H.Y., Tang, G.Y., & Liu, Y.M. (2008). Optimal vibration control for stochastic discrete-time systems. In Proceedings of the Chinese Control and Decision Conference (pp. 931–935). Yantai. doi:10.1109/CCDC.2008.4597449
  • Wu, L.G., & Wang, Z.D. (2009). Guaranteed cost control of switched systems with neutral delay via dynamic output feedback. International Journal of Systems Science, 40, 717–728. doi:10.1080/00207720902953151
  • Xie, L., Fridman, E., & Shaked, U. (2001). Robust H-infinity control of distributed delay systems with application to combustion control. IEEE Transactions on Automatic Control, 12, 1930–1935. doi:10.1109/9.975483
  • Xiao, J., Yang, Y.H., & Long, J.S. (2013). Synchronisation of complex networks with derivative coupling via adaptive control. International Journal of Systems Science, 44, 2183–2189. doi:10.1080/00207721.2012.685201
  • You, S.R., Liu, W., Lu, J.Q., Mao, X.R., & Qiu, Q.W. (2015). Stabilization of hybrid systems by feedback control based on discrete-time state observations. SIAM Journal on Control and Optimization, 2, 905–925. doi:10.1137/140985779
  • You, S.R., Hu, L.J., Mao, W.R., & Mao, X.R. (2015). Robustly exponential stabilization of hybrid uncertain systems by feedback controls based on discrete-time observations. Statistics & Probability Letters, 102, 8–12.
  • Zhu, Q.X., Rakkiyappan, R., & Chandrasekar, A. (2014). Stochastic stability of Markovian jump BAM neural networks with leakage delays and impulse control. Neurocomputing, 136, 136–151. doi:10.1016/j.neucom.2014.01.018
  • Zhu, Q.X., & Cao, J.D. (2012). Stability analysis of Markovian jump stochastic BAM neural networks with impulse control and mixed time delays. IEEE Transactions on Neural Networks and Learning Systems, 3, 467–479. doi:10.1109/TNNLS.2011.2182659
  • Zhang, C.M., Li, W.X., & Wang, K. (2013). Boundedness for network of stochastic coupled van der Pol oscillators with time-varying delayed coupling. Applied Mathematical Modelling, 7, 5394–5402. doi:10.1016/j.apm.2012.10.032

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.