Open Access


Implementation of Legendre Neural Network to Solve Time-Varying Singular Bilinear Systems

V. Murugesh1, B. Saravana Balaji2,*, Habib Sano Aliy3, J. Bhuvana4, P. Saranya5, Andino Maseleno6, K. Shankar7, A. Sasikala8
1 Department of Computer Science, College of Informatics, Bule Hora University, PO Box 144, Ethiopia
2 Department of Information Technology, Lebanese French University, Erbil, 44001, Iraq
3 Deptartment of Logistics and Supply Chain Management, Arba Minch University, Sawla Campus, PO Box 13, Ethiopia
4 Department of MCA, School of Computer Science and IT, Jain (Deemed to be) University, Bangalore, 560069, India
5 Department of Computer Science and Engineering, SRM Institute of Science and Technology, Chennai, 603203, India
6 Department of Information Systems, STMIK Pringsewu, Lampung, Indonesia
7 Department of Computer Applications, Alagappa University, Karaikudi, 630003, India
8 Department of EEE, Sri Sairam Institute of Technology, Chennai, 600044, India
* Corresponding Author: B. Saravana Balaji. Email:

Computers, Materials & Continua 2021, 69(3), 3685-3692.

Received 13 February 2021; Accepted 03 May 2021; Issue published 24 August 2021


Bilinear singular systems can be used in the investigation of different types of engineering systems. In the past decade, considerable attention has been paid to analyzing and synthesizing singular bilinear systems. Their importance lies in their real world application such as economic, ecological, and socioeconomic processes. They are also applied in several biological processes, such as population dynamics of biological species, water balance, temperature regulation in the human body, carbon dioxide control in lungs, blood pressure, immune system, cardiac regulation, etc. Bilinear singular systems naturally represent different physical processes such as the fundamental law of mass action, the DC motor, the induction motor drives, the mechanical brake systems, aerial combat between two aircraft, the missile intercept problem, modeling and control of small furnaces and hydraulic rotary multi-motor systems. The current research work discusses the Legendre Neural Network’s implementation to evaluate time-varying singular bilinear systems for finding the exact solution. The results were obtained from two methods namely the RK-Butcher algorithm and the Runge Kutta Arithmetic Mean (RKAM) method. Compared with the results attained from Legendre Neural Network Method for time-varying singular bilinear systems, the output proved to be accurate. As such, this research article established that the proposed Legendre Neural Network could be easily implemented in MATLAB. One can obtain the solution for any length of time from this method in time-varying singular bilinear systems.


Time-varying singular bilinear systems; RK-butcher algorithm; legendre neural network method

Cite This Article

V. Murugesh, B. Saravana Balaji, H. Sano Aliy, J. Bhuvana, P. Saranya et al., "Implementation of legendre neural network to solve time-varying singular bilinear systems," Computers, Materials & Continua, vol. 69, no.3, pp. 3685–3692, 2021.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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