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Higher Order Sylster’s Equation on Measure Chains-Controllability and Observability

Received: 17 June 2015     Accepted: 2 July 2015     Published: 15 July 2015
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Abstract

In this article we derive the solution of higher order Sylster’s type differential equation on measure chains in terms of two fundamental matrices. Later by defining the controllability and observability on measure chains, necessary conditions for the controllability and observability of the higher order Sylster’s type differential system on measure chains is established.

Published in American Journal of Applied Mathematics (Volume 3, Issue 4)
DOI 10.11648/j.ajam.20150304.13
Page(s) 179-184
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Measure Chains, Controllability Observability, Fundamental Matrix

References
[1] Alaa E Hamza , Karima M Oraby, Stability of abstract dynamic equations on time scales, Advances in Difference Equations 2012, 2012:143
[2] Z. Bartosiewicz and E. Pawłuszewicz, Realizations of linear control systems on time scales, Control & Cybernetics, vol. 35, no. 4, pp.769–786, 2006.
[3] J. Z. Bartosiewicz and E. Pawłuszewicz, Linear control systems on time scale: unification of continuous and discrete, in Proceedings of the 10th IEEE International Conference On Methods and Models in Automation and Robotics MMAR 2004, Miedzyzdroje, Poland, 2004.
[4] J.J. Da Cunha, Stability for time varying linear dynamic systems on time scales, J. Comput. Appl. Math. 176 (2005)381–410.
[5] V.Lakshmikantham, S.Sivasundaram and B.Kaymakclan, Dynamic systems on measure chains, Kluwer academic Publishers, (1996).
[6] R. J. Marks II, I. A. Gravagne, J. M. Davis, and J. J. Da Cunha, Nonregressivity in switched linear circuits and mechanical systems, Mathematical and Computer Modelling, vol.43, pp. 1383–1392, 2006.
[7] K.N.Murty, G.W.Howell and G.V.R.L. Sarma, Two (Multi) Point Nonlinear Lyapunov Systems Associated with an nth order Nonlinear system of differential equations-Existence and Uniqueness, Journal of Mathematical Problems In Engineering, Vol 6, Pp 395-410, 2000.
[8] K.N.Murty, Y.Narasimhulu and G.V.R.L.Sarma, Controllability and Observability of Lyapunov type Matrix Integro differential systems. International Journal of non linear differential equations: Theory, Methods and Applications, Vol 7, Nos 1& 2, pp 1 – 18, 2001.
[9] Murty K.N., Rao Y.S Two point boundary value problems inhomogeneous time scale linear dynamic process, JMAA 184(1994) pp 22-34.
[10] Nguyen Huu Du and Le Huy Tien, On the exponential stability of dynamic equations on time scales, J. Math. Anal. Appl. 331 (2007) 1159–1174.
[11] Pıtzsche, S. Sigmund, and F. Wirth, A spectral characterization of exponential stability for linear time-invariant systems on time scales, Discrete and Continuous Dynamical Systems, vol. 9, no. 5, pp. 1223–1241, 2003.
[12] Goteti V.R.L.Sarma, A new look into the Controllability and Observability of Lyapunov type matrix dynamical systems on measure chains, Global Journal of research in engineering (I) Vol XIV Issue II, Version 1, 2014 , pp 5 – 8
[13] Stephen Barnet, Introduction to mathematical control, Clarendon Press- Oxford (1975).
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  • APA Style

    Goteti V. R. L. Sarma. (2015). Higher Order Sylster’s Equation on Measure Chains-Controllability and Observability. American Journal of Applied Mathematics, 3(4), 179-184. https://doi.org/10.11648/j.ajam.20150304.13

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    ACS Style

    Goteti V. R. L. Sarma. Higher Order Sylster’s Equation on Measure Chains-Controllability and Observability. Am. J. Appl. Math. 2015, 3(4), 179-184. doi: 10.11648/j.ajam.20150304.13

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    AMA Style

    Goteti V. R. L. Sarma. Higher Order Sylster’s Equation on Measure Chains-Controllability and Observability. Am J Appl Math. 2015;3(4):179-184. doi: 10.11648/j.ajam.20150304.13

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  • @article{10.11648/j.ajam.20150304.13,
      author = {Goteti V. R. L. Sarma},
      title = {Higher Order Sylster’s Equation on Measure Chains-Controllability and Observability},
      journal = {American Journal of Applied Mathematics},
      volume = {3},
      number = {4},
      pages = {179-184},
      doi = {10.11648/j.ajam.20150304.13},
      url = {https://doi.org/10.11648/j.ajam.20150304.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150304.13},
      abstract = {In this article we derive the solution of higher order Sylster’s type differential equation on measure chains in terms of two fundamental matrices. Later by defining the controllability and observability on measure chains, necessary conditions for the controllability and observability of the higher order Sylster’s type differential system on measure chains is established.},
     year = {2015}
    }
    

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    AB  - In this article we derive the solution of higher order Sylster’s type differential equation on measure chains in terms of two fundamental matrices. Later by defining the controllability and observability on measure chains, necessary conditions for the controllability and observability of the higher order Sylster’s type differential system on measure chains is established.
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Author Information
  • Department of Mathematics, University of Dodoma, Dodoma, Tanzania

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