Publication Cover
Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 16
403
Views
14
CrossRef citations to date
0
Altmetric
Articles

Controllability of second-order nonlocal retarded semilinear systems with delay in control

&
Pages 2741-2754 | Received 04 Jan 2019, Accepted 09 Feb 2019, Published online: 19 Feb 2019

References

  • Wang L. Approximate controllability of integrodifferential equations with multiple delays. J Optim Theory Appl. 2009;143:185–206. doi: 10.1007/s10957-009-9545-0
  • Naito K. Controllability of semilinear control systems dominated by the linear part. SIAM J Control Optim. 1987;25(3):715–722. doi: 10.1137/0325040
  • Sukavanam N. Approximate controllability of semilinear control systems with growing nonlinearity. In: Mathematical Theory of Control Proceedings of International Conference. New York (NY): Marcel Dekker; 1993. p. 353–357.
  • Klamka J. Stochastic controllability and minimum energy control of systems with multiple delays in control. Appl Math Comput. 2008;206:704–715.
  • Klamka J. Stochastic controllability of systems with variable delay in control. Bull Pol Acad Tech. 2008;56(3):279–284.
  • Davies I, Jackreece P. Controllability and null controllability of linear systems. J Appl Sci Environ Manag. 2005;9:31–36.
  • Tomar NK, Kumar S. Approximate controllability of non local semilinear time-varying delay control systems. Nonlinear Dyn Syst Theory. 2012;12(3):303–310.
  • Klamka J. Controllability of linear systems with time-variable delays in control. Int J Control. 1976;24(6):869–878. doi: 10.1080/00207177608932867
  • Kumar S, Sukavanam N. Controllability of semilinear systems with fixed delay in control. Opuscula Math. 2015;35(1):71–83. doi: 10.7494/OpMath.2015.35.1.71
  • Chabrowski J. On non-local problems for parabolic equations. Nagoya Math J. 1984;93:109–131. doi: 10.1017/S0027763000020754
  • Byszewski L. Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem. J Math Anal Appl. 1991;162:494–505. doi: 10.1016/0022-247X(91)90164-U
  • Shukla A. Approximate controllability of retarded semilinear stochastic system with non local conditions. J Appl Math Comput. 2015;49:513–527. doi: 10.1007/s12190-014-0851-9
  • Arora U, Sukavanam N. Approximate controllability of second order semilinear stochastic system with nonlocal conditions. Appl Math Comput. 2015;258:111–119.
  • Klamka J, Wyrwal J. Controllability of second-order infinite-dimensional systems. Syst Control Lett. 2008;57(5):386–391. doi: 10.1016/j.sysconle.2007.10.002
  • Kumar S, Sukavanam N. Controllability of second order systems with nonlocal conditions in Banach spaces. Numer Funct Anal Optim. 2014;35:423–431. doi: 10.1080/01630563.2013.814067
  • Kumar S, Tomar NK. Mild solution and controllability of second order nonlocal retarded semilinear systems. IMA J Math Control Inform. 2018;00:1–11.
  • Travis CC, Webb GF. Cosine families and abstract nonlinear second order differential equations. Acta Math Acad Sci Hungaricae Tomus. 1978;32(3–4):75–96. doi: 10.1007/BF01902205
  • Shukla A, Sukavanam N, Pandey DN. Approximate controllability of semilinear system with state delay using sequence method. J Franklin Inst. 2015;352:5380–5392. doi: 10.1016/j.jfranklin.2015.08.019
  • Curtain RF, Zwart H. An introduction to infinite dimensional linear systems theory. New York (NY): Springer; 1995. (Texts in applied mathematics; 21).
  • Klamka J. Constrained controllability of semilinear systems with delayed controls. Bull Polish Acad Sci Tech Sci. 2008;56(4):333–337.
  • Klamka J. Constrained controllability of semilinear systems with delays. Nonlinear Dyn. 2009;56(1–2):169–177. doi: 10.1007/s11071-008-9389-4
  • Klamka J. Constrained controllability of semilinear systems with multiple delays in control. Bull Polish Acad Sci Tech Sci. 2004;52(1):25–30.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.