In this article, we consider finite dimensional dynamical control systems described by nonlinear impulsive Ito type stochastic integrodifferential equations. Necessary and sufficient conditions for complete controllability of nonlinear impulsive stochastic systems are formulated and proved under the natural assumption that the corresponding linear system is appropriately controllable. A fixed point approach is employed for achieving the required result.
@article{bwmeta1.element.bwnjournal-article-amcv19i4p589bwm,
author = {Rathinasamy Sakthivel},
title = {Controllability of nonlinear impulsive Ito type stochastic systems},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {19},
year = {2009},
pages = {589-595},
zbl = {1300.93041},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv19i4p589bwm}
}
Rathinasamy Sakthivel. Controllability of nonlinear impulsive Ito type stochastic systems. International Journal of Applied Mathematics and Computer Science, Tome 19 (2009) pp. 589-595. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv19i4p589bwm/
[000] Alotaibi, S., Sen, M., Goodwine, B. and Yang, K. T. (2004). Controllability of cross-flow heat exchangers, International Journal of Heat and Mass Transfer 47(5): 913-924. | Zbl 1083.76021
[001] Balachandran, K. and Sakthivel, R. (2001). Controllability of integrodifferential systems in Banach spaces, Applied Mathematics and Computation 118(1): 63-71. | Zbl 1034.93005
[002] Balasubramaniam, P. and Dauer, J. P. (2003). Controllability of semilinear stochastic evolution equations with time delays, Publicationes Mathematicae Debrecen 63(3): 279-291. | Zbl 1051.34065
[003] Bashirov, A. E. and Mahmudov, N. I. (1999). On concepts of controllability for deterministic and stochastic systems, SIAM Journal on Control and Optimization 37(6): 1808-1821. | Zbl 0940.93013
[004] Keck, D. N. and McKibben, M. A. (2006). Abstract semilinear stochastic Ito Volterra integrodifferential equations, Journal of Applied Mathematics and Stochastic Analysis 20(2): 1-22. | Zbl 1234.60065
[005] Klamka, J. (1991). Controllability of Dynamical Systems, Kluwer, Dordrecht. | Zbl 0732.93008
[006] Klamka, J. (2000). Schauders fixed-point theorem in nonlinear controllability problems, Control and Cybernetics 29(1): 153-165. | Zbl 1011.93001
[007] Klamka, J. (2007a). Stochastic controllability of linear systems with delay in control, Bulletin of the Polish Academy of Sciences: Technical Sciences 55(1): 23-29. | Zbl 1203.93190
[008] Klamka, J. (2007b). Stochastic controllability of linear systems with state delays, International Journal of Applied Mathematics and Computer Science 17(1): 5-13. | Zbl 1133.93307
[009] Klamka, J. and Socha, L. (1977). Some remarks about stochastic controllability, IEEE Transactions on Automatic Control 22(5): 880-881. | Zbl 0363.93048
[010] Klamka, J. and Socha, L. (1980). Some remarks about stochastic controllability for delayed linear systems, International Journal of Control 32(3): 561-566. | Zbl 0443.93011
[011] Liu, B., Liu, X. Z. and Liao, X. X. (2007). Existence and uniqueness and stability of solutions for stochastic impulsive systems, Journal of Systems Science and Complexity 20(1): 149-158. | Zbl 1124.93054
[012] Mahmudov, N. I. (2001). Controllability of linear stochastic systems, IEEE Transactions on Automatic Control 46(1): 724-731. | Zbl 1031.93034
[013] Mahmudov, N. I. and Zorlu, S. (2003). Controllability of nonlinear stochastic systems, International Journal of Control 76(2): 95-104. | Zbl 1111.93301
[014] Mahmudov, N. I. and Zorlu, S. (2005). Controllability of semilinear stochastic systems, International Journal of Control 78(13): 997-1004. | Zbl 1097.93034
[015] Mao, X. (1997). Stochastic Differential Equations and Applications, Elis Horwood, Chichester. | Zbl 0892.60057
[016] Murge, M. G. and Pachpatte, B. G. (1986a). Explosion and asymptotic behavior of nonlinear Ito type stochastic integro-differential equations, Kodai Mathematical Journal 9(1): 1-18. | Zbl 0594.60061
[017] Murge, M. G. and Pachpatte, B. G. (1986b). On generalized Ito type stochastic integral equation, Yokohama Mathematical Journal 34(1-2): 23-33. | Zbl 0626.60057
[018] Rao, A. N. V. and Tsokos, C. P. (1995). Stability of impulsive stochastic differential systems, Dynamical Systems and Applications 4(4): 317-327. | Zbl 0838.93070
[019] Respondek, J. (2005). Numerical approach to the non-linear diofantic equations with applications to the controllability of infinite dimensional dynamical systems, International Journal of Control 78(13): 1017-1030. | Zbl 1108.93021
[020] Respondek, J. S. (2007). Numerical analysis of controllability of diffusive-convective system with limited manipulating variables, International Communications in Heat and Mass Transfer 34(8): 934-944.
[021] Respondek, J. S. (2008). Approximate controllability of infinite dimensional systems of the n-th order, International Journal of Applied Mathematics and Computer Science 18(2): 199-212. | Zbl 1234.93019
[022] Sakthivel, R., Kim, J. H. and Mahmudov, N. I. (2006). On controllability of nonlinear stochastic systems, Reports on Mathematical Physics 58(3): 433-443. | Zbl 1129.93327
[023] Samoilenko, A. M. and Perestyuk, N. A. (1995). Impulsive Differential Equations, World Scientific, Singapore. | Zbl 0837.34003
[024] Sunahara, Y., Kabeuchi, T., Asad, Y., Aihara, S. and Kishino, K. (1974). On stochastic controllability for nonlinear systems, IEEE Transactions on Automatic Control 19(1): 49-54. | Zbl 0276.93011
[025] Yang, Z., Xu, D. and Xiang, L. (2006). Exponential p-stability of impulsive stochastic differential equations with delays, Physics Letters A 359(2): 129-137. | Zbl 1236.60061