In this paper, three different methods of determination of fundamental matrix of Linear control systems, when the coefficient matrix A is not a nilpotent matrix are compared. In the case where A is nilpotent, the calculation is straight forward and easy. It only needs the calculation of eAt: The methods compared, in the case of A not being nilpotent are Faddeve Algorithm method, Sylvester Expansion Theorem method and Diagonalization method. Fundamental matrix plays a very big role in the determination of solution to linear control systems. Based on this, we have to look for the best method of determining it. Here, the level of problems and difficulties encountered in determining the fundamental matrix using these three methods were verified. Worked examples on the use of these three methods to determine the fundamental matrix were given and level of problems and difficulties examined. From the worked example, it was discovered that these three methods have different level of problems and difficulties in finding the fundamental matrix. It was then concluded that based on their different level of problems and difficulties, these methods were compared and conclusion derived. These three methods which are effective ways of determining Fundamental matrix of linear control systems will be preferred in this order: Faddeve Algoprithm method, Sylvester Expansion Theorem method and Diagonalization method.
| Published in | Mathematics Letters (Volume 8, Issue 2) |
| DOI | 10.11648/j.ml.20220802.12 |
| Page(s) | 32-36 |
| 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), 2022. Published by Science Publishing Group |
Characteristic Polynomial, Eigenvalues, Eigen Vectors, Nilpotent Matrix
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APA Style
Stephen Ekwueme Aniaku, Emmanuel Chukwudi Mbah, Christopher Chukwuma Asogwa. (2022). Comparison of Results for Some Different Methods of Determination of Fundamental Matrix of Linear Control Systems. Mathematics Letters, 8(2), 32-36. https://doi.org/10.11648/j.ml.20220802.12
ACS Style
Stephen Ekwueme Aniaku; Emmanuel Chukwudi Mbah; Christopher Chukwuma Asogwa. Comparison of Results for Some Different Methods of Determination of Fundamental Matrix of Linear Control Systems. Math. Lett. 2022, 8(2), 32-36. doi: 10.11648/j.ml.20220802.12
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Download@article{10.11648/j.ml.20220802.12,
author = {Stephen Ekwueme Aniaku and Emmanuel Chukwudi Mbah and Christopher Chukwuma Asogwa},
title = {Comparison of Results for Some Different Methods of Determination of Fundamental Matrix of Linear Control Systems},
journal = {Mathematics Letters},
volume = {8},
number = {2},
pages = {32-36},
doi = {10.11648/j.ml.20220802.12},
url = {https://doi.org/10.11648/j.ml.20220802.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20220802.12},
abstract = {In this paper, three different methods of determination of fundamental matrix of Linear control systems, when the coefficient matrix A is not a nilpotent matrix are compared. In the case where A is nilpotent, the calculation is straight forward and easy. It only needs the calculation of eAt: The methods compared, in the case of A not being nilpotent are Faddeve Algorithm method, Sylvester Expansion Theorem method and Diagonalization method. Fundamental matrix plays a very big role in the determination of solution to linear control systems. Based on this, we have to look for the best method of determining it. Here, the level of problems and difficulties encountered in determining the fundamental matrix using these three methods were verified. Worked examples on the use of these three methods to determine the fundamental matrix were given and level of problems and difficulties examined. From the worked example, it was discovered that these three methods have different level of problems and difficulties in finding the fundamental matrix. It was then concluded that based on their different level of problems and difficulties, these methods were compared and conclusion derived. These three methods which are effective ways of determining Fundamental matrix of linear control systems will be preferred in this order: Faddeve Algoprithm method, Sylvester Expansion Theorem method and Diagonalization method.},
year = {2022}
}
TY - JOUR T1 - Comparison of Results for Some Different Methods of Determination of Fundamental Matrix of Linear Control Systems AU - Stephen Ekwueme Aniaku AU - Emmanuel Chukwudi Mbah AU - Christopher Chukwuma Asogwa Y1 - 2022/07/28 PY - 2022 N1 - https://doi.org/10.11648/j.ml.20220802.12 DO - 10.11648/j.ml.20220802.12 T2 - Mathematics Letters JF - Mathematics Letters JO - Mathematics Letters SP - 32 EP - 36 PB - Science Publishing Group SN - 2575-5056 UR - https://doi.org/10.11648/j.ml.20220802.12 AB - In this paper, three different methods of determination of fundamental matrix of Linear control systems, when the coefficient matrix A is not a nilpotent matrix are compared. In the case where A is nilpotent, the calculation is straight forward and easy. It only needs the calculation of eAt: The methods compared, in the case of A not being nilpotent are Faddeve Algorithm method, Sylvester Expansion Theorem method and Diagonalization method. Fundamental matrix plays a very big role in the determination of solution to linear control systems. Based on this, we have to look for the best method of determining it. Here, the level of problems and difficulties encountered in determining the fundamental matrix using these three methods were verified. Worked examples on the use of these three methods to determine the fundamental matrix were given and level of problems and difficulties examined. From the worked example, it was discovered that these three methods have different level of problems and difficulties in finding the fundamental matrix. It was then concluded that based on their different level of problems and difficulties, these methods were compared and conclusion derived. These three methods which are effective ways of determining Fundamental matrix of linear control systems will be preferred in this order: Faddeve Algoprithm method, Sylvester Expansion Theorem method and Diagonalization method. VL - 8 IS - 2 ER -
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