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2009 | 19 | 4 | 589-595

Tytuł artykułu

Controllability of nonlinear impulsive Ito type stochastic systems

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
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.

Rocznik

Tom

19

Numer

4

Strony

589-595

Opis fizyczny

Daty

wydano
2009
otrzymano
2008-10-02
poprawiono
2009-05-08

Twórcy

  • Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea

Bibliografia

  • 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.
  • Balachandran, K. and Sakthivel, R. (2001). Controllability of integrodifferential systems in Banach spaces, Applied Mathematics and Computation 118(1): 63-71.
  • Balasubramaniam, P. and Dauer, J. P. (2003). Controllability of semilinear stochastic evolution equations with time delays, Publicationes Mathematicae Debrecen 63(3): 279-291.
  • 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.
  • 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.
  • Klamka, J. (1991). Controllability of Dynamical Systems, Kluwer, Dordrecht.
  • Klamka, J. (2000). Schauders fixed-point theorem in nonlinear controllability problems, Control and Cybernetics 29(1): 153-165.
  • 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.
  • Klamka, J. (2007b). Stochastic controllability of linear systems with state delays, International Journal of Applied Mathematics and Computer Science 17(1): 5-13.
  • Klamka, J. and Socha, L. (1977). Some remarks about stochastic controllability, IEEE Transactions on Automatic Control 22(5): 880-881.
  • Klamka, J. and Socha, L. (1980). Some remarks about stochastic controllability for delayed linear systems, International Journal of Control 32(3): 561-566.
  • 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.
  • Mahmudov, N. I. (2001). Controllability of linear stochastic systems, IEEE Transactions on Automatic Control 46(1): 724-731.
  • Mahmudov, N. I. and Zorlu, S. (2003). Controllability of nonlinear stochastic systems, International Journal of Control 76(2): 95-104.
  • Mahmudov, N. I. and Zorlu, S. (2005). Controllability of semilinear stochastic systems, International Journal of Control 78(13): 997-1004.
  • Mao, X. (1997). Stochastic Differential Equations and Applications, Elis Horwood, Chichester.
  • 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.
  • Murge, M. G. and Pachpatte, B. G. (1986b). On generalized Ito type stochastic integral equation, Yokohama Mathematical Journal 34(1-2): 23-33.
  • Rao, A. N. V. and Tsokos, C. P. (1995). Stability of impulsive stochastic differential systems, Dynamical Systems and Applications 4(4): 317-327.
  • 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.
  • 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.
  • 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.
  • Sakthivel, R., Kim, J. H. and Mahmudov, N. I. (2006). On controllability of nonlinear stochastic systems, Reports on Mathematical Physics 58(3): 433-443.
  • Samoilenko, A. M. and Perestyuk, N. A. (1995). Impulsive Differential Equations, World Scientific, Singapore.
  • 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.
  • 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.

Typ dokumentu

Bibliografia

Identyfikatory

Identyfikator YADDA

bwmeta1.element.bwnjournal-article-amcv19i4p589bwm
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