Finite-time stability and stabilization of Markovian switching stochastic systems with impulsive effects

Journal of Systems Engineering and Electronics

Volumn 21, Issue 2, 2010, Pages 254-260

  Yang, Ying ^a,b   Li, Junmin ^a   Chen, Guopei ^b  

^a XIDIAN UNIVERSITY   (China)

^b HUIZHOU UNIVERSITY   (China)

Author keywords

Brownian motion; Finite time stability; Impulsive systems; Linear matrix inequalities (LMIs); Markovian switching; Stabilization

Indexed keywords

BROWNIAN MOTION; FINITE TIME STABILITY; IMPULSIVE SYSTEMS; LINEAR MATRIX; MARKOVIAN SWITCHING;

BROWNIAN MOVEMENT; CLOSED LOOP SYSTEMS; DYNAMICAL SYSTEMS; FEEDBACK; LINEAR MATRIX INEQUALITIES; STABILIZATION; STATE FEEDBACK; STOCHASTIC SYSTEMS; SWITCHING; SWITCHING SYSTEMS;

SYSTEM STABILITY;

EID: 77956272498     PISSN: 10044132     EISSN: None     Source Type: Journal    
DOI: 10.3969/j.issn.1004-4132.2010.02.014     Document Type: Article

References (23)

1. H. I. Kushner, P. Dupuis. Numerical methods for stochastic control problems in continuous time. New York: Springer-Verlag, 2001.
2. X. C. Xie, G. Wei, K. P. Wu, et al. Link reliability based hybrid routing for tactical mobile and hoc network. Journal of Systems Engineering and Electronics, 2008, 19(2): 259-267.
3. Y. Ji, H. J. Chizeck. Controllability, stability and continuoustime Markovian jump linear quadratic control. IEEE Trans. on Automatic Control, 1990, 35(7): 777-788.
4. X. Mao. Stability of stochastic differential equations with Markovian switching. Stochastic Process and Application, 1999, 79(1): 45-67.
5. L. Hu, P. Shi, B. Huang. Stochastic stability and robust control for sampled-data systems with Markovian jump parameters. Journal of Mathematical Analysis and Applications, 2006,313(2): 504-517.
6. V. Dragan, T. Morozan. Stability and robust stabilization to linear stochastic systems described by differential equations with Markovian jumping and multiplicative white noise. Stochastic Analysis and Applications, 2002, 20(1): 33-92.
7. P. Dorato. Short time stability in linear time-varying systems. Proc. of IRE International Convention Record Part 4, 1961, (1): 83-87.
8. L. Weiss, E. F. Infante. Finite time stability under perturbing forces and on product spaces. IEEE Trans. on Automatic Control, 1967, 12(1): 54-59.
9. H. D. Angelo. Linear time-varying systems: analysis and synthesis. Boston, MA: Allyn and Bacon, 1970.
10. F. Amato,M. Ariola, P. Dorato. Finite-time control of linear systems subject to parametric uncertainties and disturbances. Automatica, 2001, 37(9): 1459-1463.
11. F. Amato, M. Ariola. Finite-time control of discrete-time linear systems. IEEE Trans. on Automatic Control, 2005, 50(5): 724-729.
12. Y. G. Hong, J. K. Wang. Nonsmooth finite-time stabilization of a class of nonlinear systems. Science in China: Series E, 2005, 35(6): 663-672.
13. X. Q. Huang, W. Lin, B. Yang. Global finite-time stabilization of a class of uncertain nonlinear systems. Automatica, 2005, 41(5): 881-888. (Pubitemid 40352402)
14. H. J. Kushner. Finite-time stochastic stability and the analysis of tracking systems. IEEE Trans. on Automatic Control, 1966, 11(2): 219-227.
15. rd IEEE Conference on Decision and Control, 2004: 2572-2577.
16. L. J. Van Mellaert, P. Dorato. Numerical solution of an optimal control problem with a probability criterion. IEEE Trans. on Automatic Control, 1972, 17(4): 543-546.
17. M. A. Rami, X. Chen, J. B. Moore, et al. Solvability and asymptotic behavior of generalized Riccati equations arising in indefinite stochastic LQ controls. IEEE Trans. on Automatic Control, 2001, 46(3): 428-440.
18. H. Ye, A. N. Michel, L. Hou. Stability analysis of systems with impulse effect. IEEE Trans. on Automatic Control, 1998, 43(12): 1719-1723.
19. G. Xie, L. Wang. Necessary and sufficient conditions for controllability and observability of switched impulsive control systems. IEEE Trans. on Automatic Control, 2004, 49(6): 960-966.
20. Z. H. Guan, D. J. Hill, X. Shen. On hybrid impulsive and switching systems and application to nonlinear control. IEEE Trans. on Automatic Control, 2005, 50(7): 1058-1062.
21. Z. G. Li, C. Y. Wen, Soh Y C. Analysis and design of impulsivecontrol systems. IEEE Trans. on Automatic Control, 2001, 46(6): 894-897.
22. A. V. Skorohod. Symptotic methods in the theory of stochastic differential equations. American Mathematical Society, 2004.
23. E. K. Boukas. Stochastic hybrid systems: analysis and design. Boston: Birkhauser, 2005.