Robust delayed-state-feedback stabilization of uncertain stochastic systems

Automatica

Volumn 45, Issue 5, 2009, Pages 1332-1339

  Huang, Lirong ^a   Mao, Xuerong ^a  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Delay dependent stability; Linear matrix inequality; State feedback stabilization; Stochastic systems; Time delay

Indexed keywords

CONTROL INPUTS; DELAY-DEPENDENT STABILITY; DELAY-DEPENDENT STABILITY CRITERION; DETERMINISTIC SYSTEMS; FEEDBACK STABILIZATIONS; INPUT DELAYS; LINEAR MATRIX INEQUALITY; NUMERICAL EXAMPLES; STATE-FEEDBACK CONTROLLERS; STATE-FEEDBACK STABILIZATION; TIME SPENT; UNCERTAIN STOCHASTIC SYSTEMS;

FEEDBACK; FUZZY CONTROL; LINEAR CONTROL SYSTEMS; LINEAR MATRIX INEQUALITIES; NONLINEAR CONTROL SYSTEMS; RANDOM PROCESSES; ROBUSTNESS (CONTROL SYSTEMS); STABILITY CRITERIA; STATE FEEDBACK; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC SYSTEMS; SYSTEM STABILITY; TIME DELAY; UNCERTAIN SYSTEMS;

STABILIZATION;

EID: 65049090952     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2009.01.004     Document Type: Article

References (36)

1. Basin M.V., and Rodkina A.E. On delay-dependent stability for a class of nonlinear stochastic systems with multiple state delays. Nonlinear Analysis. Theory Methods and Applications 68 (2008) 2147-2157
2. Boyd S., EI Ghaoui L., Feron E., and Balakrishnan V. Linear matrix inequalities in systems and control (1994), SIAM, Philadelphia
3. Chen W.-H., Guan Z.-H., and Lu X. Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: An LMI approach. Systems & Control Letters 54 (2005) 547-555
4. Chen W.-H., and Zheng W.X. On improved robust stabilization of uncertain systems with unknown input delay. Automatica 42 (2006) 1067-1072
5. Feng Z., and Liu Y. Stability analysis and stabilization synthesis of stochastic large scale systems (1995), Science Press, Beijing
6. Fridman E. New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems. Systems & Control Letters 43 (2001) 309-319
7. Fridman E., and Shaked U. An improved stabilization method for linear time-delay systems. IEEE Transactions on Automatic Control 47 (2002) 1931-1937
8. ∞ control: Constant and time-varying delays. International Journal of Control 76 (2003) 48-60
9. Gu, K. (2000). An integral inequality in the stability problem of time-delay systems. In Proceedings of the 39th IEEE conference on decision and control (pp. 2805-2810)
10. Hale J.K. Theory of functional differential equations (1977), Springer-Verlag, New York
11. He Y., Wang Q.-G., Lin C., and Wu M. Delay-range-dependent stability for systems with time-varying delay. Automatica 43 (2007) 371-376
12. Huang L., and Deng F. Robust stability of perturbed large-scale multi-delay stochastic systems. Dynamics of Continuous, Discrete & Impulsive Systems. Series B 9 (2002) 525-537
13. Huang, L., & Deng, F. (2007). Robust exponential stabilization of stochastic large-scale delay systems. In Proceedings of 2007 IEEE international conference on control and automation (pp. 107-112)
14. Kim D.S., Lee Y.S., Kwon W.H., and Park P.G. Maximum allowable delay bounds of networked control systems. Control Engineering Practice 11 (2003) 1301-1313
15. Kolmanovskii V.B., and Myshkis A. Introduction to the theory and applications of functional differential equations (1999), Kluwer Academic Publishers, Dordrecht
16. ∞ control for uncertain systems with a state-delay. Automatica 40 (2004) 65-72
17. Li H., Chen B., Zhou Q., and Lin C. Delay-dependent robust stability for stochastic time-delay systems with polytopic uncertainties. International Journal of Robust and Nonlinear Control 18 (2008) 1482-1492
18. Liao X.X., and Mao X. Exponential stability of stochastic delay interval systems. Systems & Control Letters 40 (2000) 171-181
19. Luo R.C., and Chung L.-Y. Stabilization for linear uncertain system with time latency. IEEE Transactions on Industrial Electronics 49 (2002) 905-910
20. Mao X. Robustness of exponential stability of stochastic differential delay equations. IEEE Transactions on Automatic Control 41 (1996) 442-447
21. Mao X. Razumikhin-type theorems on exponential stability of stochastic functional differential equations. Stochastic Processes and their Applications 65 (1996) 233-250
22. Mao X., Koroleva N., and Rodkina A. Robust stability of uncertain stochastic differential delay equations. Systems & Control Letters 35 (1998) 325-336
23. Mao X. The LaSalle-type theorems for stochastic functional differential equations. Journal of Mathematical Analysis and Applications 7 (2000) 307-328
24. Mao X. Stochastic differential equations and applications. 2nd ed. (2007), Horwood Publishing, Chichester
25. Moon Y.S., Park P.G., and Kwon W.H. Robust stabilization of uncertain input-delayed systems using reduction method. Automatica 37 (2001) 307-312
26. Moon Y.S., Park P.G., Kwon W.H., and Lee Y.S. Delay-dependent robust stabilization of uncertain state-delayed systems. International Journal of Control 74 (2001) 1447-1455
27. Park P.G. A delay-dependent stability criterion for systems with uncertain time-invariant delays. IEEE Transactions on Automatic Control 44 (1999) 876-877
28. Rodkina A.E., and Basin M.V. On delay-dependent stability for a class of nonlinear stochastic delay-differential equations. Mathematics of Control, Signals, and Systems 18 (2006) 187-197
29. Shen Y., Luo Q., and Mao X. The improved LaSalle-type theorems for stochastic functional differential equations. Journal of Mathematical Analysis and Applications 318 (2006) 134-154
30. Xu B. Stability robustness bounds for linear systems with multiple time-varying delayed perturbations. International Journal of Systems Science 28 (1997) 1311-1317
31. ∞ control for uncertain stochastic systems with state delay. IEEE Transactions on Automatic Control 47 (2002) 2089-2094
32. Xu. S., and Lam J. Improved delay-dependent stability criteria for time-delay systems. IEEE Transactions on Automatic Control 50 (2005) 384-387
33. ∞ control of uncertain neutral stochastic time-delay systems. Journal of Mathematical Analysis and Applications 314 (2006) 1-16
34. Yue D. Robust stabilization of uncertain systems with unknown input delay. Automatica 40 (2004) 331-336
35. Yue D., and Han Q.-L. Delay-dependent exponential stability of stochastic systems with time-varying delay nonlinearity, and Markovian switching. IEEE Transactions on Automatic Control 50 (2005) 217-222
36. Yue D., and Han Q.-L. Delayed feedback control of uncertain systems with time-varying input delay. Automatica 41 (2005) 233-240