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

Goteti V. R. L. Sarma

doi:doi:10.11648/j.ajam.20150304.13

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

Goteti V. R. L. Sarma

Published in American Journal of Applied Mathematics (Volume 3, Issue 4)

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

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[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.
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[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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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},
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  number = {4},
  pages = {179-184},
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  url = {https://doi.org/10.11648/j.ajam.20150304.13},
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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.},
 year = {2015}
}

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TY  - JOUR
T1  - Higher Order Sylster’s Equation on Measure Chains-Controllability and Observability
AU  - Goteti V. R. L. Sarma
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PY  - 2015
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T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
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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

Goteti V. R. L. Sarma

Department of Mathematics, University of Dodoma, Dodoma, Tanzania

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Plain Text BibTeX RIS

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - Higher Order Sylster’s Equation on Measure Chains-Controllability and Observability
AU  - Goteti V. R. L. Sarma
Y1  - 2015/07/15
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150304.13
DO  - 10.11648/j.ajam.20150304.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 179
EP  - 184
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150304.13
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.
VL  - 3
IS  - 4
ER  -

Copy | Download