Construction of Lyapunov Functions for the Stability of Sixth Order Ordinary Differential Equation
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) $.
References
A.T. Ademola and P.O. Arawomo, Asymptotic behavior of solutions of third order nonlinear differential equations, Acta Univ. Sapientiae Math. 3(2) (2011), 197-211.
A.U. Afuwape and M.O. Omeike, Stability and boundedness of solutions of a kind of third-order delay differential equations, Comput. Appl. Math. 29(3) (2010), 329-342. https://doi.org/10.1590/S1807-03022010000300001.
J.O.C. Ezeolu and H.M. Ogbu, Construction of Lyapunov-Type of Functions for some third order Non linear ordinary differential equations by the method of integration, Journal of Science Teachers Association of Nigeria 45 (1-2) (2010), 49-58.
B.S. Ogundare, On boundedness and stability of solutions of certain third order delay differential equation, J. Nigerian Math. Soc. 31 (2012), 55-68.
D.D. Bainov and I.M. Stamova, Second method of Lyapunov and existence of periodic solutions of linear impulsive differential-difference equations, Divulg. Mat. 5(1-2) (1997), 29-37.
R. Jingli, C. Wing-Sum and C. Zhibo, Existence and Lyapunov stability of periodic solutions for generalized higher-order neutral Differential Equations, Boundary Value Problems, volume 2011 Article ID635767, 21 pages. https://doi.org/10.1155/2011/635767
Lars Grne, Peter E. Kloeden, Stefan Siegmund and Fabian R. Wirth, Lyapunov's second method for nonautonomous differential equations, Discrete & Continuous Dynamical Systems 18(23) (2007), 375-403. https://doi.org/10.3934/dcds.2007.18.375
Mohamed Harmouche, Salah Laghrouche and Yacine Chitour, Stabilization of perturbed integrator chains using Lyapunov-Based homogeneous controllers, arXiv : 1303.5330v3 [math.OC] 30th May 2013
B. O. Orie, Construction of Lyapunov functions for some fourth order nonlinear ordinary differential equations by method of integration, International Journal of Scientific and Technology Research 3(10) (2014), 275-285.
P. C. Parks, A. M. Lyapunov's stability theory - 100 years on, IMA Journal of Mathematical Control and Information 9(4) (1992), 275-303. https://doi.org/10.1093/imamci/9.4.275
Patrick O. Aye, D. Jayeola and David O. Oyewola, Construction of Lyapunov functions for the stability of fifth order nonlinear ordinary differential equations, Earthline Journal of Mathematical Sciences 8(2) (2022), 313-324. https://doi.org/10.34198/ejms.8222.313324
This work is licensed under a Creative Commons Attribution 4.0 International License.
.jpg){kind=logo}
