Controllability, Observability and Stability of Volterra Type Non-Linear Matrix Integro-Dynamic System on Time Scales

  • Authors

    • G V. Ramana
    • G V. S. R. Deekshitulu
    2018-08-24
    https://doi.org/10.14419/ijet.v7i3.31.18278
  • Controllability, non-linear Volterra type matrix integro-dynamic system, observability, stability, time scales.

  • Abstract

    This paper investigates the controllability, observability and stability of the solution of Volterra type non linear matrix integro dynamic system on time scales.

     

     

  • References

    1. [1] M. Adivar, “Principal matrix solution and variation of

      parameters for Volterra integro-dynamic equations on time

      scalesâ€, Glasg. Math. J, Vol.53, (2011), pp.463-480.

      [2] L.C. Becker, “Principal matrix solutions and variation of parameters for a for Volterra-integro-differential equation and

      its adjointâ€, Electron J Qual Theory Differ Equ, Vol.14,

      (2006), pp.1-22.

      [3] M. Bohner, A. Peterson, Dynamic Equations on Time Scales,

      Birkhauser, Boston, (2001).

      [4] T.A. Burton, W.E. Mahfound, “Stability criteria for Volterra

      equationsâ€,Trans Am Math Soc Vol.279, (1983), pp.143-174.

      [5] T.A. Burton, W.E. Mahfound, “Stability by decompositions

      for Volterra equationsâ€, Tohoku Math J JI Ser Vol.37, (1985),

      pp.489-511.

      [6] T.A. Burton, Volterra integral and differential equations, 2nd

      edn. Elsevier, (2005).

      [7] J.M. Davis, I.A. Gravagne, B.J.Jackson, R.J. Marks,

      “Controllability, observability, realizability, and stability of

      dynamic linear systemsâ€, Electron J Differ Equ Vol.37,

      (2009), pp.1-32.

      [8] S. Hilger, Ein Mabkettenkalkul mit Anwendung auf

      Zentrumsmannigfaltigkeiten, PhD thesis, Universitat

      Wurzburg, (1988).

      [9] IA. Gravagne, JM. Devis and JJ. Dacunha, “A unified

      approach to high-gain adaptive controllersâ€, J.Abstr Appl

      Anal, (2009).

      [10] IA. Gravagne, JM. Devis and JJ. Dacunha, RJ II. Marks,

      “Bandwidth reduction for controller area networks using

      adaptive samplingâ€, New Orleans, (2004), pp.5250-5255.

      [11] IA. Gravagne, JM. Devis and RJ II. Marks, “How

      deterministic must a real time controllerâ€,Alberta, (2005),

      pp.3856-3861.

      [12] R.E. Kalman, “On the general theory of control

      systemâ€,Proc.1st IFAC Congress Automatic control Vol.1,

      (1960), pp.481-492.

      [13] R.E. Kalman, Y.C. Ho, K.S. Narendra, “Controllability of

      linear dynamical systemsâ€,Contrib. Differ. Equ Vol.1,

      (1963), pp.189-213.

      [14] RJ II. Marks, IA. Gravagne, JM. Devis and JJ. Dacunha,

      “Nonregressivity in switching linear circuits and mechanical

      systemsâ€,Math Comput Model Vol.43, (2006), p.1383-1392.

      [15] J. Seiffert, S. Sanyal, DC. Wunsch,“Hamilton –Jacobi

      -Bellman equations and approximate dynamic programming

      • on time scalesâ€,IEEE Trans Syst Man Cybern Vol.38, (2008),

      pp.918-923.

      [16] A. Yonus, Ghaus ur Rahman, “Controllability, Observability,

      and Stability of a Volterra integro-dynamic system on time

      scalesâ€,IEEE Trans Syst Man Cybern Vol.20, (2014),

      pp.383-402.

  • Downloads

  • How to Cite

    V. Ramana, G., & V. S. R. Deekshitulu, G. (2018). Controllability, Observability and Stability of Volterra Type Non-Linear Matrix Integro-Dynamic System on Time Scales. International Journal of Engineering & Technology, 7(3.31), 115-120. https://doi.org/10.14419/ijet.v7i3.31.18278

    Received date: 2018-08-25

    Accepted date: 2018-08-25

    Published date: 2018-08-24