Abstract and Applied Analysis

Complete Controllability of Impulsive Stochastic Integrodifferential Systems in Hilbert Space

Xisheng Dai and Feng Yang

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Abstract

This paper concerns the complete controllability of the impulsive stochastic integrodifferential systems in Hilbert space. Based on the semigroup theory and Burkholder-Davis-Gundy's inequality, sufficient conditions of the complete controllability for impulsive stochastic integro-differential systems are established by using the Banach fixed point theorem. An example for the stochastic wave equation with impulsive effects is presented to illustrate the utility of the proposed result.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 783098, 7 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393511983

Digital Object Identifier
doi:10.1155/2013/783098

Mathematical Reviews number (MathSciNet)
MR3081615

Zentralblatt MATH identifier
07095351

Citation

Dai, Xisheng; Yang, Feng. Complete Controllability of Impulsive Stochastic Integrodifferential Systems in Hilbert Space. Abstr. Appl. Anal. 2013 (2013), Article ID 783098, 7 pages. doi:10.1155/2013/783098. https://projecteuclid.org/euclid.aaa/1393511983


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References

  • N. I. Mahmudov, “Controllability of linear stochastic systems,” IEEE Transactions on Automatic Control, vol. 46, no. 5, pp. 724–731, 2001.
  • A. Arapostathis, R. K. George, and M. K. Ghosh, “On the controllability of a class of nonlinear stochastic systems,” Systems & Control Letters, vol. 44, no. 1, pp. 25–34, 2001.
  • K. Balachandran and S. Karthikeyan, “Controllability of nonlinear Itô type stochastic integrodifferential systems,” Journal of the Franklin Institute, vol. 345, no. 4, pp. 382–391, 2008.
  • K. Balachandran and S. Karthikeyan, “Controllability of sto-chastic integrodifferential systems,” International Journal of Control, vol. 80, no. 3, pp. 486–491, 2007.
  • G. da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, vol. 44 of Encyclopedia of Mathematics and Its Ap-plications, Cambridge University Press, Cambridge, UK, 1992.
  • N. I. Mahmudov, “Controllability of linear stochastic systems in Hilbert spaces,” Journal of Mathematical Analysis and Applications, vol. 259, no. 1, pp. 64–82, 2001.
  • M. A. Dubov and B. S. Mordukhovich, “On controllability of infinite dimensional linear stochastic systems,” in Proceedings of the 2nd IFAC Symposium on Stochastic Control, pp. 307–310, Vilnius, Lithuania, May 1986.
  • N. I. Mahmudov, “Controllability of semilinear stochastic systems in Hilbert spaces,” Journal of Mathematical Analysis and Applications, vol. 288, no. 1, pp. 197–211, 2003.
  • J. P. Dauer and N. I. Mahmudov, “Controllability of stochastic semilinear functional differential equations in Hilbert spaces,” Journal of Mathematical Analysis and Applications, vol. 290, no. 2, pp. 373–394, 2004.
  • J. Y. Park, P. Balasubramaniam, and N. Kumaresan, “Controllability for neutral stochastic functional integrodifferential infinite delay systems in abstract space,” Numerical Functional Analysis and Optimization, vol. 28, no. 11-12, pp. 1369–1386, 2007.
  • R. Subalakshmi, K. Balachandran, and J. Y. Park, “Controllability of semilinear stochastic functional integrodifferential systems in Hilbert spaces,” Nonlinear Analysis: Hybrid Systems, vol. 3, no. 1, pp. 39–50, 2009.
  • K. Balachandran and J. P. Dauer, “Controllability of nonlinear systems in Banach spaces: a survey,” Journal of Optimization Theory and Applications, vol. 115, no. 1, pp. 7–28, 2002.
  • P. Balasubramaniam and J. P. Dauer, “Controllability of semilinear stochastic delay evolution equations in Hilbert spaces,” International Journal of Mathematics and Mathematical Sciences, vol. 31, no. 3, pp. 157–166, 2002.
  • V. Lakshmikantham, D. D. Baǐnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6 of Series in Modern Applied Mathematics, World Scientific, Singapore, 1989.
  • R. Sakthivel, N. I. Mahmudov, and J. H. Kim, “Approximate controllability of nonlinear impulsive differential systems,” Re-ports on Mathematical Physics, vol. 60, no. 1, pp. 85–96, 2007.
  • M. Li, M. Wang, and F. Zhang, “Controllability of impulsive functional differential systems in Banach spaces,” Chaos, Solitons and Fractals, vol. 29, no. 1, pp. 175–181, 2006.
  • Y.-K. Chang, “Controllability of impulsive functional differential systems with infinite delay in Banach spaces,” Chaos, Soli-tons and Fractals, vol. 33, no. 5, pp. 1601–1609, 2007.
  • R. Sakthivel, N. I. Mahmudov, and J. H. Kim, “On controllability of second order nonlinear impulsive differential systems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 1-2, pp. 45–52, 2009.
  • S. Karthikeyan and K. Balachandran, “Controllability of nonlinear stochastic neutral impulsive systems,” Nonlinear Analysis: Hybrid Systems, vol. 3, no. 3, pp. 266–276, 2009.
  • R. Sakthivel, N. I. Mahmudov, and S.-G. Lee, “Controllability of non-linear impulsive stochastic systems,” International Journal of Control, vol. 82, no. 5, pp. 801–807, 2009.
  • R. Sakthivel, “Controllability of nonlinear impulsive Itô type stochastic systems,” International Journal of Applied Mathematics and Computer Science, vol. 19, no. 4, pp. 589–595, 2009.
  • L. Shen, J. Shi, and J. Sun, “Complete controllability of impulsive stochastic integro-differential systems,” Automatica, vol. 46, no. 6, pp. 1068–1073, 2010.
  • R. Subalakshmi and K. Balachandran, “Approximate controllability of nonlinear stochastic impulsive integrodifferential sys-tems in Hilbert spaces,” Chaos, Solitons and Fractals, vol. 42, no. 4, pp. 2035–2046, 2009.