Stabilisation of hybrid stochastic differential equations by delay feedback control

Systems and Control Letters

Volumn 57, Issue 11, 2008, Pages 927-935

  Mao, Xuerong ^a   Lam, James ^b   Huang, Lirong ^a  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Brownian motion; Exponential mean square stability; Linear Matrix inequality; Markov chain

Indexed keywords

DIFFERENTIATION (CALCULUS); FEEDBACK CONTROL; MEASUREMENT THEORY; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC PROGRAMMING;

BROWNIAN MOTION; EXPONENTIAL MEAN-SQUARE STABILITY; LINEAR MATRIX INEQUALITY; MARKOV CHAIN; STABILISATION;

DIFFERENCE EQUATIONS;

EID: 50949092185     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2008.05.002     Document Type: Article

References (32)

1. Basak G.K., Bisi A., and Ghosh M.K. Stability of a random diffusion with linear drift. Journal of Mathematical Analysis and Applications 202 (1996) 604-622
2. Berman A., and Plemmons R.J. Nonnegative Matrices in the Mathematical Sciences (1994), SIAM
3. Boyd S., EI Ghaoul L., Feron R., and Balakrishnan V. Linear Matrix Inequalities in System and Control Theory (1994), SIAM
4. Chen W., Guan Z., and Lu X. Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: an LMI approach. Systems Control Letters 54 (2005) 547-555
5. ∞ performance analysis for continuous-time stochastic systems with polytopic uncertainties. Circuits Systems Signal Processing 24 (2005) 415-429
6. Has'minskii R.Z. Stochastic Stability of Differential Equations (1981), Sijthoff and Noordhoff
7. He H., Ho D.W.C., and Lam J. Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays. Institute of Electrical and Electronics Engineers Transaction on Circuits and Systems II: Express Briefs 52 (2005) 251-255
8. Ji Y., and Chizeck H.J. Controllability, stabilizability and continuous-time Markovian jump linear quadratic control. Institute of Electrical and Electronics Engineers Transactions on Automatic Control 35 (1990) 777-788
9. Kolmanovskii V.B., and Myshkis A. Applied Theory of Functional Differential Equations (1992), Kluwer Academic Publishers
10. Ladde G.S., and Lakshmikantham V. Random Differential Inequalities (1980), Academic Press
11. Mao X. Stability of Stochastic Differential Equations with Respect to Semimartingales (1991), Longman Scientific and Technical
12. Mao X. Exponential Stability of Stochastic Differential Equations (1994), Marcel Dekker
13. Mao X. Stochastic Differential Equations and Their Applications (1997), Horwood Pub, Chichester
14. Mao X. Stability of stochastic differential equations with Markovian switching. Stochastic Processes and their Applications 79 (1999) 45-67
15. Mao X. Stochastic functional differential equations with Markovian switching. Functional Differential Equations 6 3-4 (1999) 375-396
16. Mao X. Exponential stability of stochastic delay interval systems with Markovian switching. Institute of Electrical and Electronics Engineers Transactions on Automatic Control 47 10 (2002) 1604-1612
17. Mao X. Stability and stabilization of stochastic differential delay equations. IET Control Theory & Applications 1 6 (2007) 1551-1566
18. Mao X., Lam J., Xu S., and Gao H. Razumikhin method and exponential stability of hybrid stochastic delay interval systems. Journal of Mathematical Analysis and Applications 314 (2006) 45-66
19. Mao X., Matasov A., and Piunovskiy A.B. Stochastic differential delay equations with Markovian switching. Bernoulli 6 1 (2000) 73-90
20. Mao X., Yin G., and Yuan C. Stabilization and destabilization of hybrid systems of stochastic differential equations. Automatica 43 (2007) 264-273
21. Mao X., and Yuan C. Stochastic Differential Equations with Markovian Switching (2006), Imperial College Press
22. Mariton M. Jump Linear Systems in Automatic Control (1990), Marcel Dekker
23. Mohammed S.-E.A. Stochastic Functional Differential Equations (1986), Longman Scientific and Technical
24. Niu Y., Ho D.W.C., and Lam J. Robust integral sliding mode control for uncertain stochastic systems with time-varying delay. Automatica 41 (2005) 873-880
25. Shaikhet L. Stability of stochastic hereditary systems with Markov switching. Theory of Stochastic Processes 2 18 (1996) 180-184
26. Shi P., Mahmoud M.S., Yi J., and Ismail A. Worst case control of uncertain jumping systems with multi-state and input delay information. Information Sciences 176 (2006) 186-200
27. Sun M., Lam J., Xu S., and Zou Y. Robust exponential stabilization for Markovian jump systems with mode-dependent input delay. Automatica 43 (2007) 1799-1807
28. ∞ control of stochastic time-delay jumping systems with nonlinear disturbances. Optimal Control Applications & Methods 27 (2006) 255-271
29. ∞ output feedback control for uncertain stochastic systems with time-varying delays. Automatica 40 (2004) 2091-2098
30. Xu S., Lam J., Mao X., and Zou Y. A new LMI condition for delay-dependent robust stability of stochastic time-delay systems. Asian Journal of Control 7 4 (2005) 419-423
31. ∞ control for uncertain stochastic time-delay systems via non-fragile controllers. Asian Journal of Control 8 (2006) 197-200
32. Yue D., and Han Q. Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and Markovian switching. Institute of Electrical and Electronics Engineers Transactions on Automatic Control 50 (2005) 217-222