Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching

Stochastic Processes and their Applications

Volumn 118, Issue 8, 2008, Pages 1385-1406

  Mao, Xuerong ^a   Shen, Yi ^b   Yuan, Chenggui ^c  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

^b HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^c SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

Asymptotic stability; Brownian motion; Exponential stability; Generalized It formula; Markov chain

Indexed keywords

ASYMPTOTIC ANALYSIS; DIFFERENCE EQUATIONS; MATHEMATICAL MORPHOLOGY; STOCHASTIC PROGRAMMING; SYSTEM STABILITY;

(E ,2E) THEORY; ELSEVIER (CO); MARKOVIAN SWITCHING; STOCHASTIC DIFFERENTIAL DELAY EQUATIONS;

ASYMPTOTIC STABILITY;

EID: 46049098408     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2007.09.005     Document Type: Article

References (29)

1. Athans M. Command and control (c2) theory: A challenge to control science. IEEE Trans. Automat. Control 32 (1987) 286-293
2. Basak G.K., Bisi A., and Ghosh M.K. Stability of a random diffusion with linear drift. J. Math. Anal. Appl. 202 (1996) 604-622
3. Berman A., and Plemmons R. Nonnegative Matrices in the Mathematical Sciences (1994), SIAM, Philadelphia
4. Dragan V., and Morozan T. Stability and robust stabilization to linear stochastic systems described by differential equations with Markovian jumping and multiplicative white noise. Stochastic Anal. Appl. 20 (2002) 33-92
5. Gao Z.Y., and Ahmed N.U. Feedback stabilizability of nonlinear stochastic systems with state-dependent noise. Internat. J. Control 45 (1987) 729-737
6. Ghosh M.K., Arapostathis A., and Marcus S.I. Optimal control of switching diffusions with applications to flexible manufacturing systems. SIAM J. Control Optim. 31 (1993) 1183-1204
7. Hale J.K., and Lunel S.M.V. Introduction to Functional Differential Equations (1993), Springer, New York
8. Has'minskii R.Z. Stochastic Stability of Differential Equations (1981), Sijthoff and Noordhoff, Alphen
9. ∞ output feedback controller design for linear systems with time-varying delayed state. IEEE Trans. Automat. Control 43 (1998) 971-974
10. Ji Y., and Chizeck H.J. Controllability, stabilizability and continuous-time Markovian jump linear quadratic control. IEEE Trans. Automat. Control 35 (1990) 777-788
11. Kazangey T., and Sworder D.D. Effective federal policies for regulating residential housing. The Proc. Summer Computer Simulation Conference, San diego (1971) 1120-1128
12. Kolmanovskii V.B., Koroleva N., Maizenberg T., Mao X., and Matasov A. Neutral stochastic differential delay equations with Markovian switching. Stochastic Anal. Appl. 21 (2003) 819-847
13. Kolmanovskii V.B., and Nosov V.R. Stability and Periodic Modes of Control Systems with Aftereffect (1981), Nauka, Moscow
14. Lipster R.Sh., and Shiryayev A.N. Theory of Martingales (1989), Kluwer Academic Publishers
15. Mao X. Stochastic Differential Equations and Applications (1997), Horwood, England
16. Mao X. Stability of stochastic differential equations with Markovian switching. Stochastic Process. Appl. 79 (1999) 45-67
17. Mao X., Matasov A., and Piunovskiy A.B. Stochastic differential delay equations with Markovian switching. Bernoulli 6 (2000) 73-90
18. Mao X. Asymptotic properties of neutral stochastic differential delay equations. Stoch. Stoch. Rep. 68 (2000) 273-295
19. Mao X. A note on the LaSalle-type theorems for stochastic differential delay equations. J. Math. Anal. Appl. 268 (2002) 125-142
20. Mariton M. Jump Linear Systems in Automatic Control (1990), Marcel Dekker, New York
21. Moerder D.D., Halyo N., Braussard J.R., and Caglayan A.K. Application of precomputed control laws in a reconfigurable aircraft flight control system. J. Guid. Control Dyn. 12 (1989) 325-333
22. Pakshin P.V. Robust stability and stabilization of family of jumping stochastic systems. Nonlinear Anal. 30 (1997) 2855-2866
23. Pan G., and Bar-Shalom Y. Stabilization of jump linear Gaussian systems without mode observations. Internat. J. Control 64 (1996) 631-661
24. Shaikhet L. Stability of stochastic hereditary systems with Markov switching. Theory Stoch. Process. 2 (1996) 180-184
25. Skorohod A.V. Asymptotic Methods in the Theory of Stochastic Differential Equations (1989), American Mathematical Society, Providence
26. Sworder D.D., and Rogers R.O. An LQ-solution to a control problem associated with a solar thermal central receiver. IEEE Trans. Automat. Control 28 (1983) 971-978
27. A.S. Willsky, B.C. Levy, Stochastic stability research for complex power systems, DOE Contract, LIDS, MIT, Rep. ET-76-C-01-2295, 1979
28. Willems J.L., and Willems J.C. Feedback stabilizability for stochastic systems with state and control dependent noise. Automatica 12 (1976) 343-357
29. Yuan C., Zou J., and Mao X. Stability in distribution of stochastic differential delay equations with Markovian switching. Systems Control Lett. 5 (2003) 195-207