Controllability of nonlinear integrodifferential systems in Banach space

  • K. Balachandran
  • J. P. Dauer
  • P. Balasubramaniam
Contributed Papers

Abstract

Sufficient conditions for controllability of nonlinear integrodifferential systems in a Banach space are established. The results are obtained using the Schauder fixed-point theorem.

Key Words

Controllability nonlinear systems integrodifferential systems 

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References

  1. 1.
    Chukwu, E. N., andLenhart, S. M.,Controllability Questions for Nonlinear Systems in Abstract Spaces, Journal of Optimization Theory and Applications, Vol. 68, pp. 437–462, 1991.Google Scholar
  2. 2.
    Nakagiri, S., andYamamoto, M.,Controllability and Observability of Linear Retarded Systems in Banach Spaces, International Journal of Control, Vol. 49, pp. 1489–1504, 1989.Google Scholar
  3. 3.
    Naito, K.,Controllability of Semilinear Control Systems Dominated by the Linear Part, SIAM Journal on Control and Optimization, Vol. 25, pp. 715–722, 1987.Google Scholar
  4. 4.
    Naito, K.,Approximate Controllability for Trajectories of Semilinear Control Systems, Journal of Optimization Theory and Applications, Vol. 60, pp. 57–65, 1989.Google Scholar
  5. 5.
    Naito, K.,On Controllability for a Nonlinear Volterra Equation, Nonlinear Analysis: Theory, Methods and Applications, Vol. 18, pp. 99–108, 1992.Google Scholar
  6. 6.
    Naito, K., andPark, J. Y.,Approximate Controllability for Trajectories of a Delay Volterra Control System, Journal of Optimization Theory and Applications, Vol. 61, pp. 271–279, 1989.Google Scholar
  7. 7.
    Zhou, H. X.,Approximate Controllability for a Class of Semilinear Abstract Equations, SIAM Journal on Control and Optimization, Vol. 21, pp. 551–565, 1983.Google Scholar
  8. 8.
    Triggiani, R.,Controllability, Observability, and Stabilizability of Dynamical Systems in Banach Space with Bounded Operators, PhD Thesis, University of Michigan, Ann Arbor, Michigan, 1973.Google Scholar
  9. 9.
    Triggiani, R.,Controllability and Observability in Banach Spaces with Bounded Operators, SIAM Journal on Control, Vol. 13, pp. 462–491, 1975.Google Scholar
  10. 10.
    Lasiecka, I., andTriggiani, R.,Exact Controllability of Semilinear Abstract Systems with Application to Waves and Plates Boundary Control Problems, Applications of Mathematical Optimization, Vol. 23, pp. 109–154, 1991.Google Scholar
  11. 11.
    Quinn, M. D., andCarmichael, N.,An Approach to Nonlinear Control Problems Using Fixed-Point Methods, Degree Theory, and Pseudo-Inverses, Numerical Functional Analysis and Optimization, Vol. 7, pp. 197–219, 1984–1985.Google Scholar
  12. 12.
    Kwun, Y. C., Park, J. Y., andRyu, J. W.,Approximate Controllability and Controllability for Delay Volterra Systems, Bulletin of the Korean Mathematics Society, Vol. 28, pp. 131–145, 1991.Google Scholar
  13. 13.
    Nussbaum, R. P.,The Fixed-Point Index and Asymptotic Fixed-Point Theorems for k-Set Contractions, Bulletin of the American Mathematical Society, Vol. 75, pp. 490–495, 1969.Google Scholar
  14. 14.
    Fitzgibbon, W. E.,Semilinear Integrodifferential Equations in a Banach Space, Nonlinear Analysis: Theory, Methods and Applications, Vol. 4, pp. 745–760, 1980.Google Scholar
  15. 15.
    Heard, M. L.,An Abstract Semilinear Hyperbolic Volterra Integrodifferential Equation, Journal of Mathematical Analysis and Applications, Vol. 80, pp. 175–202, 1981.Google Scholar
  16. 16.
    Hussain, M. A.,On a Nonlinear Integrodifferential Equation in Banach Space, Indian Journal of Pure and Applied Mathematics, Vol. 19, pp. 516–529, 1988.Google Scholar
  17. 17.
    Miller, R. K.,Volterra Integral Equations in a Banach Space, Funkcialaj Ekvacioj, Vol. 18, pp. 163–193, 1975.Google Scholar
  18. 18.
    Pazy, A.,Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer Verlag, New York, New York, 1983.Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • K. Balachandran
    • 1
  • J. P. Dauer
    • 2
  • P. Balasubramaniam
    • 1
  1. 1.Department of MathematicsBharathiar UniversityCoimbatoreIndia
  2. 2.Department of MathematicsUniversity of Tennessee at ChattanoogaChattanoogaTennessee

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