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), 2024. Published by Science Publishing Group |
Characteristic Polynomial, Eigenvalues, Eigen Vectors, Nilpotent Matrix
| [1] | E. B. Lee and L. Markus. Foundation of optimal control theory. John Wiley and Sons New York. 1967. |
| [2] | Davis S. Watkins: Fundamentals of Matrix Computations. Second Edition. John Willey and Sons Inc. 2002. |
| [3] | J. Chen: On improved method of computation of Fundamental matrix. IEEE Conference Publication. 2007. |
| [4] | B. T. Johansson: Properties of methods of Fundamentals solutions for the parabolic heat equation. Aston publication Explorer - Aston University. 2017. |
| [5] | Xin Sheng Li and Xuedong Yuan: Automatic computation of Fundamental Matrix Base on Voting. International Conference on Smart Multimedia KSM. Smart Multimedia 2018. pp. 291-296. |
| [6] | K. Kanatani: Compact Fundamental Matrix Computation. Semantic Scholar 2009. |
| [7] | F. Feng: An Improved Method to estimate the Fundamental Matrix based on 7 - point algorithm. Semantic Scholar 2012. |
| [8] | Gil Ben - Artzi; Tavi Hlperin; Michael Werman and Shmuel Peleg: Two points Fundamental Matrix. Research Gate 2016. |
| [9] | D. Barragan: AnEA - Based Method for estimating the Fundamental Matrix. Springer Link. https://link.springer.com 2015. |
| [10] | W. Hui: Some problems with the method solution using radial basis functions; ANU College of Engineering and Computer Science (2007). |
| [11] | Frank Ayres, Jr: Schaums's Outline of Theory and Problems of Matrices. S. I Edition. Mc Graw - Hill Book Company. New York. (1974). |
| [12] | R. Kent Nagle: Fundamentals of Differential Equations, Second Edition. The Benjamin Cummings Publishing Company Inc. Califonia. (1989). |
| [13] | Chi - Tsong Chen: Linear Systems Theory and Design. Holt, Rinchart and Winston Holt - Saunders. Japan. (1984). |
| [14] | E. A Coddington and N. Levinson: Theory of Ordinary Differential Equations. Mc Graw - Hill Book Company, New York. London. (1955). |
| [15] | Lee W. Johnson. et al: Introduction to Linear Algebra. Addison - Wesley Company. Canada (1998). |
| [16] | W. E Boyce and R. C. Diprima: Elementary Differential Equations and Boundry Value Problems. Fifth Edition. John Willey and Sons, Inc. Canada (1992). |
| [17] | K. Viswanadh et al: Stability Analysis of Linear Sylvester System of First Order Differential Equations. International Journal of Engineering and Computer Science. 9 (11) (2020) pp. 25252-25259. |
| [18] |
S. E Aniaku et al A Necessary And Sufficient Condition For Matrix Solution Φ(t) of  (t)= A(t)Φ(t) To Be A Fundamental Matrix. European Modern Studies Journal 5 (6) (2021) pp. 176-183.
|
| [19] | A. Chater and A. Lasfer: New Approach To calculating The Fundamental Matrix. International Journal of Electrical and Computer Engineering (IJECE) 10 (3) (2020) pp. 2357-2366. |
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
Share This Article
Twitter
Linked In
Facebook
Copy
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 -
Information
Email: