Theory of stochastic dissipative systems

IEEE Transactions on Automatic Control

Volumn 56, Issue 7, 2011, Pages 1650-1655

  Wu, Zhaojing ^a   Cui, Mingyue ^a   Xie, Xuejun ^b   Shi, Peng ^c,d  

^a YANTAI UNIVERSITY   (China)

^b QUFU NORMAL UNIVERSITY   (China)

^c UNIVERSITY OF GLAMORGAN   (United Kingdom)

^d VICTORIA UNIVERSITY   (Australia)

Author keywords

Dissipative systems; nonlinear systems; stochastic systems

Indexed keywords

DISSIPATIVE SYSTEMS; DISSIPATIVITY; ESCAPE TIME; EXIT TIME; NON-LINEAR STOCHASTIC SYSTEMS; NON-SMOOTH; PHYSICAL MODEL;

ENERGY DISSIPATION; LYAPUNOV METHODS; MODELS; STABILITY CRITERIA; STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

DISPLAY DEVICES;

EID: 79960118505     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2011.2121370     Document Type: Article

References (25)

1. J. C.Willems, "Dissipative dynamical systems, part I: General theory," Archive Rat. Mech. Anal., vol. 45, pp. 321-351, 1972.
2. D. Hill and P. Moylan, "The stability of nonlinear dissipative systems," IEEE Trans. Autom. Control, vol. AC-21, no. 5, pp. 708-711, Oct. 1976.
3. J. C.Willems, "Paradigms and puzzles in the theory of dynamical systems," IEEE Trans. Autom. Control, vol. 36, no. 3, pp. 259-294, Mar. 1991.
4. A. L. Chen, G. Q. Chen, and R. A. Freeman, "Stability of nonlinear feedback systems: A new small-gain theorem," SIAM J. Control Optim., vol. 46, pp. 1995-2012, 2007.
5. R. Sepulchre, R. Jankovic, and P. V. Kokotović, Constructive Nonlinear Control. New York: Springer, 1997.
6. ∞-Gain and Passivity in Nonlinear Control. Secaucus, NJ: Springer-Verlag, 1999.
7. B. Brogliato, R. Lozano, B. Maschke, and O. Egeland, Dissipative Systems Analysis and Control: Theory and Applications. Secaucus, NJ: Springer-Verlag, 2000.
8. J. C. Willems, "Dissipative dynamical systems," Eur. J. Control, vol. 13, pp. 134-151, 2007.
9. U. H. Thygesen, "On dissipation in stochastic systems," in Proc. Amer. Control Conf., San Diego, CA, 1999, pp. 1430-1434.
10. V. Borkar and S. Mitter, A Note on Stochastic Dissipativeness, Directions in Math. Systems Theory and Optimization, Lecture Notes in Control Inform. No. 286. Berlin, Germany: Springer, 2003, pp. 41-49.
11. ∞ control for a class of nonlinear stochastic systems," SIAM J. Control Optim., vol. 44, pp. 1973-1991, 2006. (Pubitemid 44775247)
12. H. K. Khalil, Nonlinear Systems, 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 2002.
13. X. Mao and C.Yuan, Stochastic Differential Equations With Markovian Switching. London, U.K.: Imperial College Press, 2006.
14. Z. J. Wu, X. J. Xie, P. Shi, and Y. Q. Xia, "Backstepping controller design for a class of stochastic nonlinear systems with markovian switching," Automatica, vol. 45, pp. 997-1004, 2009.
15. M. Krstić and H. Deng, Stability of Nonlinear Uncertain Systems. New York: Springer, 1998.
16. H. Deng, M. Krstić, and R.Williiams, "Stabilization of stochastic nonlinear driven by noise of unknown covariance," IEEE Trans. Autom. Control, vol. 46, no. 8, pp. 1237-1245, Aug. 2001.
17. X. Yu and X. J. Xie, "Output feedback regulation of stochastic nonlinear systems with stochastic iISS inverse dynamics," IEEE Trans. Autom. Control, vol. 55, no. 2, pp. 304-320, Feb. 2010.
18. C. Yuan and X. Mao, "Robust stability and controllability of stochastic differential delay equations with markovian switching," Automatica, vol. 40, pp. 343-354, 2004.
19. P. V. Pakshin, "Dissipativity of diffusion itô processes with markovain switching and problems of robust stabilization," Autom. Remote Control, vol. 68, pp. 1502-1518, 2007.
20. X. Mao, Stochastic Differential Equations and Applications. New York: Horwood, 1997.
21. P. Florchinger, "A passive system approach to feedback stabilization of nonlinear control stochastic systems," SIAM J. Control Optim., vol. 37, pp. 1848-1864, 1999. (Pubitemid 32262054)
22. R. Z. Khas'minskii, Stochastic Stability of Differential Equations. Rockville, MD: S & N Int. Publisher, 1980.
23. P. Ioannou and J. Sun, Robust Adaptive Control. Englewood Cliffs, NJ: Prentice-Hall, 1996.
24. M. Krstić, I. Kanellakopoulos, and P. V. Kokotović, Nonlinear and Adaptive Control Design. New York: Wiley, 1995.
25. F. C. Klebaner, Introduction to Stochastic Calculus With Applications. London, U.K.: Imperial College Press, 1998.