Output-feedback stabilization of stochastic high-order nonlinear systems under weaker conditions

SIAM Journal on Control and Optimization

Volumn 49, Issue 3, 2011, Pages 1262-1282

  Li, Wuquan ^a   Xie, Xue Jun ^b   Zhang, Siying ^c  

^a LUDONG UNIVERSITY   (China)

^b QUFU NORMAL UNIVERSITY   (China)

^c NORTHEASTERN UNIVERSITY   (China)

Author keywords

Nonlinear growth condition; Output feedback stabilization; Power order restriction; Stochastic high order nonlinear systems

Indexed keywords

BACK-STEPPING DESIGN METHOD; GLOBALLY ASYMPTOTICALLY STABLE; HIGH-ORDER NONLINEAR SYSTEM; HOMOGENEOUS DOMINATION; NONLINEAR FUNCTIONS; NONLINEAR GROWTH; ORDER RESTRICTION; OUTPUT-FEEDBACK; OUTPUT-FEEDBACK STABILIZATION PROBLEM;

BACKSTEPPING; NONLINEAR SYSTEMS; STABILIZATION; STOCHASTIC SYSTEMS;

NONLINEAR FEEDBACK;

EID: 79960367156     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/100798259     Document Type: Article

References (31)

1. M. KRSTIĆ AND H. DENG, Stabilization of Uncertain Nonlinear Systems, Springer, New York, 1998.
2. M. KRSTIĆ AND H. DENG, Output-feedback stochastic nonlinear stabilization, IEEE Trans. Automat. Control, 44(1999), pp. 328-333.
3. H. DENG AND M. KRSTIĆ, Output-feedback stabilization of stochastic nonlinear systems driven by noise of unknown covariance, Systems Control Lett., 39(2000), pp. 173-182.
4. S. J. LIU, J. F. ZHANG, AND Z. P. JIANG, Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems, Automatica J. IFAC, 43(2007), pp. 238-251.
5. S. J. LIU, Z. P. JIANG, AND J. F. ZHANG, Global output-feedback stabilization for a class of stochastic non-minimum-phase nonlinear systems, Automatica J. IFAC, 44(2008), pp. 1944-1957.
6. S. J. LIU AND J. F. ZHANG, Output-feedback control of a class of stochastic nonlinear systems with linearly bounded unmeasurable states, Internat. J. Robust Nonlinear Control, 18(2008), pp. 665-687.
7. Z. PAN AND T. BAŞAR, Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion, SIAM J. Control Optim., 37(1999), pp. 957-995.
8. Y. G. LIU AND J. F. ZHANG, Reduced-order observer-based control design for nonlinear stochastic systems, Systems Control Lett., 52(2004), pp. 123-135.
9. Y.-G. LIU AND J.-F. ZHANG, Practical output-feedback risk-sensitive control for stochastic nonlinear systems with stable zero-dynamics, SIAM J. Control Optim., 45(2006), pp. 885-926. (Pubitemid 46796960)
10. X. YU AND X. J. XIE, Output feedback regulation of stochastic nonlinear systems with stochastic iISS inverse dynamics, IEEE Trans. Automat. Control, 55(2010), pp. 304-320.
11. X. YU, X.-J. XIE, AND N. DUAN, Small-gain control method for stochastic nonlinear systems with stochastic iISS inverse dynamics, Automatica J. IFAC, 46(2010), pp. 1790-1798.
12. N. DUAN, X. YU, AND X.-J. XIE, Output feedback control using small-gain conditions for stochastic nonlinear systems with SiISS inverse dynamics, Internat. J. Control, 84(2011), pp. 47-56.
13. X. YU, X. J. XIE, AND Y. Q. WU, Further results on output-feedback regulation of stochastic nonlinear systems with SiISS inverse dynamics, Internat. J. Control, 83(2010), pp. 2140-2152.
14. W. LIN, Wei Lin's Homepage, http://nonlinear.cwru.edu/~linwei/ (2009).
15. C. J. QIAN, Global Synthesis of Nonlinear Systems with Uncontrollable Linearization, Ph. D. Dissertation, Department of Electrical and Computer Science, Case Western Reserve University, Cleveland, OH, 2001.
16. X. J. XIE AND J. TIAN, State-feedback stabilization for high-order stochastic nonlinear systems with stochastic inverse dynamics, Internat. J. Robust Nonlinear Control, 17(2007), pp. 1343-1362. (Pubitemid 47425432)
17. J. TIAN AND X. J. XIE, Adaptive state feedback stabilization for high-order stochastic nonlinear systems with uncertain control coefficients, Internat. J. Control, 80(2007), pp. 1503-1516. (Pubitemid 47460784)
18. X. J. XIE AND J. TIAN, Adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization, Automatica J. IFAC, 45(2009), pp. 126-133.
19. W. Q. LI, Y. W. JING, S. Y. ZHANG, AND G. M. DIMIROVSKI, State-feedback stabilization for high-order stochastic nonlinear systems without strict triangular conditions, in Proceedings of the 2010 American Control Conference, IEEE Press, Piscataway, NJ, 2010, pp. 367-372.
20. W. Q. LI, Y. W. JING, AND S. Y. ZHANG, Decentralized stabilization of a class of large-scale high-order stochastic nonlinear systems, IET Control Theory Appl., 4(2010), pp. 2441-2453.
21. W. Q. LI AND X. J. XIE, Inverse optimal stabilization for stochastic nonlinear systems whose linearizations are not stabilizable, Automatica J. IFAC, 45(2009), pp. 498-503.
22. X.-J. XIE AND N. DUAN, Output tracking of high-order stochastic nonlinear systems with application to benchmark mechanical system, IEEE Trans. Automat. Control, 55(2010), pp. 1197-1202.
23. X. J. XIE AND W. Q. LI, Output-feedback control of a class of high-order stochastic nonlinear systems, Internat. J. Control, 82(2009), pp. 1692-1705.
24. C. J. QIAN AND W. LIN, Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization, Systems Control Lett., 42(2001), pp. 185-200. (Pubitemid 32663822)
25. C. J. QIAN, A homogeneous domination approach for global output feedback stabilization of a class of nonlinear systems, in Proceedings of the 2005 American Control Conference, IEEE Press, Piscataway, NJ, 2005, pp. 4708-4715.
26. C. J. QIAN AND J. LI, Global output feedback stabilization of upper-triangular nonlinear systems using a homogeneous domination approach, Internat. J. Robust Nonlinear Control, 16(2006), pp. 441-463. (Pubitemid 43835623)
27. J. POLENDO AND C. J. QIAN, A generalized framework for global output feedback stabilization of nonlinear systems, in Proceedings of the 44th Annual IEEE Conference on Decision and Control, IEEE Press, Piscataway, NJ, 2005, pp. 2646-2651. (Pubitemid 46297371)
28. J. POLENDO AND C. J. QIAN, A generalized homogeneous domination approach for global stabilization of inherently nonlinear systems via output feedback, Internat. J. Robust Nonlinear Control, 17(2007), pp. 605-629. (Pubitemid 46616429)
29. J. KURZWEIL, On the inversion of Lyapunov's second theorem on the stability of motion, Amer. Math. Soc. Transl., 2(1956), pp. 19-77.
30. L. ROSIER, Homogeneous Lyapunov function for homogeneous continuous vector field, Systems Control Lett., 19(1992), pp. 467-473. (Pubitemid 23617374)
31. B. YANG AND W. LIN, Homogeneous observers, iterative design and global stabilization of high order nonlinear systems by smooth output feedback, IEEE Trans. Automat. Control, 49(2004), pp. 1069-1080.