Construction of Lyapunov Functions for the Stability of Sixth Order Ordinary Differential Equation
Open Access
- 1 September 2022
- journal article
- Published by Earthline Publishers in Earthline Journal of Mathematical Sciences
- Vol. 10 (2), 423-438
- https://doi.org/10.34198/ejms.10222.423438
Abstract
This study employed Lyapunov function method to investigate the stability of nonlinear ordinary differential equations. Using Lyapunov direct method, we constructed Lyapunov function to investigate the stability of sixth order nonlinear ordinary differential equations. We find $ V(x) $, a quadratic form, positive definite and $ U(x) $ which is also positive definite was chosen such that the derivative of $ V(x) $ with respect to time was equal to the negative value of $ U(x) $.
Keywords
This publication has 6 references indexed in Scilit:
- Construction of Lyapunov Functions for the Stability of Fifth Order Nonlinear Ordinary Differential EquationsEarthline Journal of Mathematical Sciences, 2022
- Boundedness and asymptotic behaviour of solutions of a nonlinear differential equation of the third orderAfrika Matematika, 2011
- Existence and Lyapunov Stability of Periodic Solutions for Generalized Higher-Order Neutral Differential EquationsBoundary Value Problems, 2011
- Stability and boundedness of solutions of a kind of third-order delay differential equationsComputational and Applied Mathematics, 2010
- Lyapunov's second method for nonautonomous differential equationsDiscrete & Continuous Dynamical Systems, 2007
- A. M. Lyapunov's stability theory—100 years onIMA Journal of Mathematical Control and Information, 1992