State Feedback Stabilization of Stochastic Feedforward Nonlinear Systems with Input Time-delay
-
摘要: 针对一类具有输入时滞的随机前馈非线性系统, 首次研究了它的状态反馈镇定问题. 首先引入一个变量变换, 将其与齐次占优方法巧妙结合, 通过构造合适的 Lyapunov-Krasovskii 泛函, 设计了一个状态反馈控制器, 使得闭环系统的平衡点依概率全局渐近稳定.
-
关键词:
- 随机前馈系统 /
- 输入时滞 /
- Lyapunov-Krasovskii 泛函 /
- 状态反馈镇定
Abstract: In this paper, the problem of state feedback stabilization for stochastic feedforward nonlinear systems with input time-delay is considered for the first time. By introducing a variable transformation, skillfully combining the homogeneous domination method, and constructing an appropriate Lyapunov Krasovskii functional, a state feedback controller is developed to guarantee the closed-loop system globally asymptotically stable in probability. -
[1] Krstić M, Deng H. Stabilization of Nonlinear Uncertain Systems. New York: Springer-Verlag, 1998. [2] Deng H, Krstić M, Williams R J. Stabilization of stochastic nonlinear systems driven by noise of unknown covariance. IEEE Transactions on Automatic Control, 2001, 46(8): 1237-1253 [3] Mao X R. Stochastic Differential Equations and Their Applications. Chichester: Horwood Publishing, 2007. [4] Fu Y S, Tian Z H, Shi S J. Output-feedback stabilization for a class of stochastic time-delay nonlinear systems. IEEE Transactions on Automatic Control, 2005, 50(6): 847-850 [5] Liu S J, Ge S Z, Zhang J F. Adaptive output-feedback control for a class of uncertain stochastic non-linear systems with time delays. International Journal of Control, 2008, 81(8): 1210-1220 [6] Liu L, Xie X J. Output-feedback stabilization for stochastic high-order nonlinear systems with time-varying delay. Automatica, 2011, 47(12): 2772-2779 [7] Xie X J, Liu L. Further result on output feedback stabilization for stochastic high-order nonlinear systems with time-varying delay. Automatica, 2012, 48(9): 2577-2586 [8] Xie X J, Liu L. A homogeneous domination approach to state feedback of stochastic high-order nonlinear systems with time-varying delay. IEEE Transactions on Automatic Control, 2013, 58(2): 494-499 [9] Qian C J. A homogeneous domination approach for global output feedback stabilization of a class of nonlinear systems. In: Proceedings of the 2005 American Control Conference. Portland, USA: IEEE, 2005. 4708-4715 [10] Liu L, Xie X J. State feedback stabilization for stochastic feedforward nonlinear systems with time-varying delay. Automatica, 2013, 49(4): 936-942 [11] Zhao C R, Xie X J. Global stabilization of stochastic high-order feedforward nonlinear systems with time-varying delay. Automatica, 2014, 50(1): 203-210 [12] Michiels W, Niculescu S I. Stability and Stabilization of Time-Delay Systems: An Eigenvalue-Based Approach. Singapore: SIAM, 2007. [13] Liu S J. Controller Design for Stochastic Nonlinear Systems and Performance Analysis of the Closed-Loop Systems [Ph. D. dissertation], Chinese Academy of Sciences, China, 2009. (in Chinese) [14] Zhang X F. Stabilization of Nonlinear Time-Delay Systems in Triangular Form [Ph. D. dissertation], Shandong University, China, 2005. (in Chinese) [15] Zhang X F, Cheng Z L. Output feedback stabilization of nonlinear systems with delays in the input. Applied Mathematics and Computation, 2005, 167(2): 1026-1040 [16] Zhang X F, Boukas E K, Liu Y G, Baron L. Asymptotic stabilization of high-order feedforward systems with delays in the input. International Journal of Robust and Nonlinear Control, 2010, 20(12): 1395-1406 [17] Khalil H K. Nonlinear Systems. Beijing: Publishing House of Electronics Industry, 2007.
点击查看大图
计量
- 文章访问数: 1420
- HTML全文浏览量: 64
- PDF下载量: 782
- 被引次数: 0