Stability of hybrid stochastic retarded systems

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 55, Issue 11, 2008, Pages 3413-3420

  Huang, Lirong ^a   Mao, Xuerong ^a   Deng, Feiqi ^b  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

^b SOUTH CHINA UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Asymptotic stability; Markov chain; Razumikhintype theorems; Retarded systems; Stochastic systems

Indexed keywords

ASYMPTOTIC STABILITY; DIFFERENTIAL EQUATIONS; MARKOV CHAINS; SYSTEM STABILITY;

INTERVAL SYSTEMS; ITS APPLICATIONS; MARKOVIAN SWITCHING; RAZUMIKHIN-TYPE THEOREM; RETARDED SYSTEM; STOCHASTIC DELAY; STOCHASTIC DELAY SYSTEMS; STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATION;

STOCHASTIC SYSTEMS;

EID: 58049192406     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2008.2001825     Document Type: Article

References (22)

1. D. Chatterjee and D. Liberzon, "On stability of randomly switched nonlinear systems," IEEE Trans. Autom. Control, vol. 52, no. 12, pp. 2390-2394, Dec. 2007.
2. Z. Feng and Y. Liu, Stability Analysis and Stabilization Synthesis of Stochastic Large Scale Systems. Beijing, China: Science Press, 1995.
3. J. K. Hale, Theory of Functional Differential Equations. New York: Springer-Verlag, 1977.
4. I. A. Hiskens, "Power system modeling for inverse problems," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 51, no. 4, pp. 539-551, Apr. 2004.
5. L. Huang and F. Deng, "Robust stability of perturbed large-scale multidelay stochastic system," Dynam. Contin. Discreet, Impulsive Syst. B, vol. 9, pp. 525-537, 2002.
6. V. B. Kolmanovskii and V. R. Nosov, Stability of Functional Differential Equations. New York: Academic, 1986.
7. V. B. Kolmanovskii and A. Myshkis, Introduction to the Theory and Applications of Functional Differential Equations. Dordrecht, The Netherlands: Kluwer Academic, 1999.
8. J. Krupar and W. Schwarz, "EMI tuning of hybrid systems by periodic patterns," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 53, no. 9, pp. 2060-2067, Sep. 2006.
9. G. S. Ladde, "Differential inequalities and stochastic functional differential equations," J. Math. Phys., vol. 15, pp. 738-743, 1974.
10. H. Lin and P. J. Antsaklis, "Switching stabilizability for continuous-time uncertain switched linear systems," IEEE Trans. Autom. Control, vol. 52, pp. 633-646, 2007.
11. X. Mao, Stochastic Differential Equations and Applications. Chichester, U.K.: Horwood Publishing, 1997.
12. X. Mao, "Stochastic functional differential equations with Markovian switching," Functional Differential Equations, vol. 6, pp. 375-396, 1999.
13. X. Mao, A. Matasov, and A. B. Piunovskiy, "Stochastic differential delay equations with Markovian switching," Bernoulli, vol. 6, pp. 73-90, 2000.
14. X. Mao and L. Shaikhet, "Delay-dependent stability criteria for stochastic differential delay equations with Markovian switching," Stab. Control: Theory Appl., vol. 3, pp. 87-101, 2000.
15. X. Mao, "Exponential stability of stochastic delay interval systems with Markovian switching," IEEE Trans. Autom. Control, vol. 47, pp. 1604-1612, 2002.
16. X. Mao, J. Lam, S. Xu, and H. Gao, "Razumikhin method and exponential stability of hybrid stochastic delay interval systems," J. Math. Anal. Appl., vol. 314, pp. 45-66, 2006.
17. A. V. Skorohod, Asymptotic Methods in the Theoryof Stochastic Differential Equations. Providence, RI: Amer. Math. Society, 1989.
18. X. Sun, W. Wang, G.-P. Liu, and J. Zhao, "Stability analysis for linear switched systems with time-varying delay," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 38, pp. 528-533, 2008.
19. Z. Sun, "A note on marginal stability of switched systems," IEEE Trans. Autom. Control, vol. 53, pp. 625-631, 2008.
20. B. Xu, "Necessary and sufficient conditions of generalized exponential stability for retarded dynamic systems," J. Control Theory Appl., vol. 16, pp. 802-806, 1999.
21. B. Xu, "Stability of retarded dynamic systems: A Lyapunov function approach," J. Math. Anal. Appl., vol. 253, pp. 590-615, 2001.
22. D. Yue and Q.-L. Han, "Delay-dependent exponential stability of stochastic equations with time-varying delay, nonlinearity, and Markovian switching," IEEE Trans. Autom. Control, vol. 50, pp. 217-222, 2005.