Complete controllability of impulsive stochastic integro-differential systems

Automatica

Volumn 46, Issue 6, 2010, Pages 1068-1073

  Shen, Lijuan ^a,b   Shi, Junping ^c   Sun, Jitao ^a  

^a TONGJI UNIVERSITY   (China)

^b LUOYANG NORMAL UNIVERSITY   (China)

^c The College of William and Mary   (United States)

Author keywords

Complete controllability; Impulsive stochastic systems; Integro differential systems; Schaefer's fixed point theorem

Indexed keywords

FIXED POINT THEOREMS; IMPULSIVE STOCHASTIC SYSTEMS; INTEGRO-DIFFERENTIAL SYSTEM; NUMERICAL EXAMPLE; SCHAEFER'S FIXED POINT THEOREM; SUFFICIENT CONDITIONS;

CONTROLLABILITY; STOCHASTIC SYSTEMS;

DIFFERENTIAL EQUATIONS;

EID: 77953157368     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2010.03.002     Document Type: Article

References (27)

1. Balachandran K., and Karthikeyan S. Controllability of nonlinear Ito type stochastic integrodifferential systems. Journal of the Franklin Institute 345 4 (2008) 382-391
2. Balachandran K., Karthikeyan S., and Kim J.H. Controllability of semilinear stochastic integrodifferential systems. Kybernetika 43 1 (2007) 31-44
3. Bemporad A., Ferrari-Trecate G., and Morari M. Observability and controllability of piecewise affine and hybrid systems. IEEE Transactions on Automatic Control 45 10 (2000) 1864-1876
4. Conway J.B. A course in functional analysis (1990), Springer-Verlag, New York
5. Dong Y.W., and Sun J.T. On hybrid control of a class of stochastic non-linear Markovian switching systems. Automatica 44 4 (2008) 990-995
6. Guan Z.H., Qian T.H., and Yu X.H. On controllability and observability for a class of impulsive systems. Systems & Control Letters 47 3 (2002) 247-257
7. Karthikeyan S., and Balachandran K. Controllability of nonlinear stochastic neutral impulsive systems. Nonlinear Analysis. Hybrid Systems 3 3 (2009) 266-276
8. Lakshmikantham V., Bainov D.D., and Simeonov P.S. Theory of impulsive differential equations (1989), World Scientific, Singapore
9. Li T.T., and Rao B.P. Exact boundary controllability for quasi-linear hyperbolic systems. SIAM Journal on Control and Optimization 41 6 (2003) 1748-1755
10. Li M.L., Wang M.S., and Zhang F.Q. Controllability of impulsive functional differential systems in Banach spaces. Chaos, Solitons & Fractals 29 1 (2006) 175-181
11. Liu B. Stability of solutions for stochastic impulsive systems via comparison approach. IEEE Transactions on Automatic Control 53 9 (2008) 2128-2133
12. Liu B., and Marquez H.J. Controllability and observability for a class of controlled switching impulsive systems. IEEE Transactions on Automatic Control 53 10 (2008) 2360-2366
13. Mahmudov N.I. Controllability of linear stochastic systems. IEEE Transactions on Automatic Control 46 5 (2001) 724-731
14. Mahmudov N.I. Controllability of linear stochastic systems in Hilbert spaces. Journal of Mathematical Analysis and Applications 259 1 (2001) 64-82
15. Mahmudov N.I. Approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces. SIAM Journal on Control and Optimization 42 5 (2003) 1604-1622
16. Mahmudov N.I., and Zorlu S. Controllability of non-linear stochastic systems. International Journal of Control 76 2 (2003) 95-104
17. Mao X. Stochastic differential equations and applications (1997), Horwood, Chichester, UK
18. Niu Y.G., Ho D.W.C., and Wang X.Y. Sliding mode control for Ito stochastic systems with Markovian switching. Automatica 43 10 (2007) 1784-1790
19. Oksendal B. Stochastic differential equations. 6th ed. (2003), Springer-Verlag
20. Sakthivel R., Kim J.H., and Mahmudov N.I. On controllability of nonlinear stochastic systems. Reports on Mathematical Physics 58 3 (2006) 433-443
21. Sakthivel R., Mahmudov N.I., and Kim J.H. On controllability of second order nonlinear impulsive differential systems. Nonlinear Analysis 71 (2009) 45-52
22. Sakthivel R., Mahmudov N.I., and Lee S.G. Controllability of non-linear impulsive stochastic systems. International Journal of Control 82 5 (2009) 801-807
23. Smart D.R. Fixed point theorem (1980), Cambridge Univ. Press, Cambridge
24. Subalakshmi R., and Balachandran K. Approximate controllability of nonlinear stochastic impulsive integrodifferential systems in hilbert spaces. Chaos, Solitons & Fractals 42 4 (2009) 2035-2046
25. ∞ control for a class of nonlinear discrete time-delay stochastic systems with missing measurements. Automatica 45 3 (2009) 684-691
26. Xie G.M., and Wang L. Necessary and sufficient conditions for controllability and observability of switched impulsive control systems. IEEE Transactions on Automatic Control 49 6 (2004) 960-966
27. Zhao P. Practical stability, controllability and optimal control of stochastic Markovian jump systems with time-delays. Automatica 44 12 (2008) 3120-3125