Finite-time state-feedback control for a class of stochastic high-order nonlinear systems

References

• W. Ai, J. Zhai, and S. Fei, Global finite-time stabilization for a class of stochastic nonlinear systems by dynamic state feedback, Kybernetika 49(4) (2013), pp. 590–600.
   Web of Science ®Google Scholar
• S.P. Bhat and D.S. Bernstein, Finite-time stability of continuous autonomous systems, SIAM J. Control Optim. 38(3) (2000), pp. 751–766. doi: 10.1137/S0363012997321358
   Web of Science ®Google Scholar
• H. Deng and M. Krstić, Stochastic nonlinear stabilization-I: A backstepping design, Systems Control Lett. 32(3) (1997), pp. 143–150. doi: 10.1016/S0167-6911(97)00068-6
   Web of Science ®Google Scholar
• H. Deng, M. Krstić, and R.J. Williams, Stabilization of stochastic nonlinear systems driven by noise of unknown covariance, IEEE Trans. Automat. Control 46(8) (2001), pp. 1237–1253. doi: 10.1109/9.940927
   Web of Science ®Google Scholar
• P. Florchinger, Lyapunov-like techniques for stochastic stability, SIAM J. Control Optim. 33(4) (1995), pp. 1151–1169. doi: 10.1137/S0363012993252309
   Web of Science ®Google Scholar
• Y. Hong, J. Wang, and D. Chen, Adaptive finite-time control of nonlinear systems with parametric uncertainty, IEEE Trans. Automat. Control 51(5) (2006), pp. 858–862. doi: 10.1109/TAC.2006.875006
   Web of Science ®Google Scholar
• X. Huang, W. Lin, and B. Yang, Global finite-time stabilization of a class of uncertain nonlinear systems, Automatica 41(5) (2005), pp. 881–888. doi: 10.1016/j.automatica.2004.11.036
   Web of Science ®Google Scholar
• R.Z. Khas'minskii, Stochastic Stability of Differential Equations, S&N International Publisher, Rockville, MD, 1980.
   Google Scholar
• S. Khoo, J. Yin, Z. Man, and X. Yu, Finite-time stabilization of stochastic nonlinear systems in strict-feedback form, Automatica 49(5) (2013), pp. 1403–1410. doi: 10.1016/j.automatica.2013.01.054
   Web of Science ®Google Scholar
• F. Li and Y. Liu, Global stability and stabilization of more general stochastic nonlinear systems, J. Math. Anal. Appl. 413(2) (2014), pp. 841–855. doi: 10.1016/j.jmaa.2013.12.021
   Web of Science ®Google Scholar
• W. Li, Y. Jing, and S. Zhang, Output-feedback stabilization for stochastic nonlinear systems whose linearizations are not stabilizable, Automatica 46(4) (2010), pp. 752–760. doi: 10.1016/j.automatica.2010.01.033
   Web of Science ®Google Scholar
• J. Li, C. Qian, and S. Ding, Global finite-time stabilisation by output feedback for a class of uncertain nonlinear systems, Internat. J. Control 83(11) (2010), pp. 2241–2252. doi: 10.1080/00207179.2010.511658
   Web of Science ®Google Scholar
• W. Li, X. Liu, and S. Zhang, Further results on adaptive state-feedback stabilization for stochastic high-order nonlinear systems, Automatica 48(8) (2012), pp. 1667–1675. doi: 10.1016/j.automatica.2012.05.035
   Web of Science ®Google Scholar
• L. Liu and N. Duan, State-feedback stabilization for stochastic high-order nonlinear systems with a ratio of odd integers power, Nonlinear Anal. Model. Control 15(1) (2010), pp. 39–53.
   Web of Science ®Google Scholar
• Y. Liu and J. Zhang, Practical output-feedback risk-sensitive control for stochastic nonlinear systems with stable zero-dynamics, SIAM J. Control Optim. 45(3) (2006), pp. 885–926. doi: 10.1137/S0363012903439185
   Web of Science ®Google Scholar
• X. Mao, Stochastic Differential Equations and Applications, 2nd ed., Horwood, Chichester, UK, 2007.
   Google Scholar
• E. Moulay and W. Perruquetti, Finite time stability and stabilization of a class of continuous systems, Math. Anal. Appl. 323(2) (2006), pp. 1430–1443. doi: 10.1016/j.jmaa.2005.11.046
   Web of Science ®Google Scholar
• E. Moulay and W. Perruquetti, Finite time stability conditions for non-autonomous continuous systems, Internat. J. Control 81(5) (2008), pp. 797–803. doi: 10.1080/00207170701650303
   Web of Science ®Google Scholar
• Z. Pan and T. Basar, Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion, SIAM J. Control Optim. 37(3) (1999), pp. 957–995. doi: 10.1137/S0363012996307059
   Web of Science ®Google Scholar
• Y. Shen and Y. Huang, Global finite-time stabilisation for a class of nonlinear systems, Internat. J. Systems Sci. 43(1) (2012), pp. 73–78. doi: 10.1080/00207721003770569
   Web of Science ®Google Scholar
• A.V. Skorokhod, Studies in the Theory of Random Processes, Addison-Wesley, Reading, MA, 1965.
   Google Scholar
• X. Xie and J. Tian, State-feedback stabilization for high-order stochastic nonlinear systems with stochastic inverse dynamics, Internat. J. Robust Nonlinear Control 17(14) (2007), pp. 1343–1362. doi: 10.1002/rnc.1177
   Web of Science ®Google Scholar
• S. Xie and L. Xie, Decentralized Stabilization of a class of interconnected stochastic nonlinear systems, IEEE Trans. Automat. Control 45(1) (2000), pp. 132–137. doi: 10.1109/9.827370
   Web of Science ®Google Scholar
• J. Yin, S. Khoo, Z. Man, and X. Yu, Finite-time stability and instability of stochastic nonlinear systems, Automatica 47(12) (2011), pp. 2671–2677. doi: 10.1016/j.automatica.2011.08.050
   Web of Science ®Google Scholar
• W. Zha, J. Zhai, and S. Fei, Output feedback control for a class of stochastic high-order nonlinear systems with time-varying delays, Internat. J. Robust Nonlinear Control (2013); 10.1002/rnc.2985.
   Web of Science ®Google Scholar
• J. Zhai, Decentralised output-feedback control for a class of stochastic non-linear systems using homogeneous domination approach, IET Control Theory Appl. 7(8) (2013), pp. 1098–1109. doi: 10.1049/iet-cta.2012.0868
   Web of Science ®Google Scholar
• J. Zhai, Global finite-time output feedback stabilisation for a class of uncertain non-triangular nonlinear systems, Internat. J. Systems Sci. 45(3) (2014), pp. 637–646. doi: 10.1080/00207721.2012.724113
   Web of Science ®Google Scholar