Delay-dependent exponential stability of neutral stochastic delay systems

IEEE Transactions on Automatic Control

Volumn 54, Issue 1, 2009, Pages 147-152

  Huang, Lirong ^a   Mao, Xuerong ^a  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Exponential stability; Linear matrix inequalitys (LMIs); Neutral systems; Stochastic systems; Time delay

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; LINEAR CONTROL SYSTEMS; LINEAR MATRIX INEQUALITIES; RANDOM PROCESSES; STABILITY; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC SYSTEMS; TIME DELAY;

DELAY DEPENDENTS; DELAY-DEPENDENT CRITERION; EXPONENTIAL STABILITY; LINEAR MATRIX INEQUALITY APPROACHES; LINEAR MATRIX INEQUALITYS (LMIS); NEUTRAL SYSTEMS; NUMERICAL EXAMPLES; STOCHASTIC DELAY SYSTEMS; TECHNICAL NOTES;

SYSTEM STABILITY;

EID: 59649088082     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2008.2007178     Document Type: Article

References (21)

1. W.-H. Chen, Z.-H. Guan, and X. Lu, "Delay-dependent exponential stability of uncertain uncertain stochastic systems with multiple delays," Syst. Control Lett., vol. 54, pp. 547-555, 2005.
2. W.-H. Chen and W. X. Zheng, "Stability analysis and H∞-control of delayed neutral stochastic systems with time-varying parameter uncertainties," in Proc. 45th IEEE Conf. Decision Control, San Diego, CA, Dec. 2006, pp. 961-966.
3. W.-H. Chen and W. X. Zheng, "Delay-dependent robust stabilization for uncertain neutral systems with distributed delays," Automatica, vol. 43, pp. 95-104, 2007.
4. E. Fridman, "New Lyapunov-Krasovskii functionals for stability of linear redarded and neutral type systems," Syst. Control Lett., vol. 43, pp. 309-319, 2001.
5. E. Fridman and U. Shaked, "A descriptor system approach to H∞ control of linear time-delay systems," IEEE Trans. Automat. Control, vol. 47, no. 2, pp. 253-270, Feb. 2002.
6. K. Gu, "An integral inequality in the stability problem of time-delay systems," in Proc. 39th IEEE Conf. Decision Control, Sydney, Australia, Dec. 2000, pp. 2850-2810.
7. J. K. Hale, Theory of Functional Differential Equations. New York: Springer-Verlag, 1977.
8. Q.-L. Han, "A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays," Automatica, vol. 40, pp. 1791-1796, 2004.
9. Y. He, Q.-G. Wang, C. Lin, and M. Wu, "Augmented Lyapunov functional and delay-dependent stability criteria for neutral systems," Int. J. Robust Nonlin. Control, pp. 923-933, Nov. 2005.
10. V. B. Kolmanovskii and A. Myshkis, Introduction to the Theory and Applications of Functional Differential Equations. Dordrecht, The Netherlands: Kluwer, 1999.
11. C.-H. Lien, K.-W. Wu, and J.-G. Hsieh, "Stability conditions for a class of neutral systems with multiple time delays," J. Math. Anal. Appl., vol. 245, pp. 20-27, 2000.
12. Q. Luo, X. Mao, and Y. Shen, "New criteria on exponential stability of neutral stochastic differential equations," Syst. Control Lett., vol. 55, pp. 826-834, 2006.
13. M. S. Mahmoud, "Robust H∞ control of linear neutral systems," Automatica, vol. 36, pp. 757-764, 2000.
14. X. Mao, "Exponential stability in mean square of neutral stochastic differential functional equations," Syst. Control Lett., vol. 26, pp. 245-251, 1995.
15. X. Mao, "Razumikhin-type theorems on exponential stability of neutral stochastic functional differential equations," SIAM J. Math. Anal. vol. 28, pp. 389-401, 1997a.
16. X. Mao, Stochastic Differential Equations and Applications. Chichester, U.K.: Horwood Publishing, 1997.
17. X. Mao, "Asymptotic properties of neutral stochastic differential delay equations," Stochastics Stochastics Rep., vol. 68, pp. 273-295, 2000.
18. S.-I. Niculescu, "Further remarks on delay-dependent stability of linear neutral systems," in Proc. MTNS'00, Perpigan, France, 2000.
19. J. H. Park and S.Won, "Stability analysis for neutral delay-differential systems," J. Franklin Inst., vol. 337, pp. 1-9, 2000.
20. B. Xu, "Stability robustness bounds for linear systems with multiple time-varying delayed perturbations," Int. J. Syst. Sci., vol. 28, pp. 1311-1317, 1997.
21. ∞ control of uncertain neutral stochastic time-delay systems," J. Math. Anal. Appl., vol. 314, pp. 1-16, 2006.