TITLE:
Lyapunov Stability Analysis of Certain Third Order Nonlinear Differential Equations
AUTHORS:
R. N. Okereke
KEYWORDS:
Nonlinear ODE, Energy, Lyapunov Function, Assymptotic Stability
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.16,
October
25,
2016
ABSTRACT: This paper is concerned with the stability
analysis of nonlinear third order ordinary differential equations of the form .
We construct a suitable Lyapunov function for this purpose and show that it guarantees asymptotic stability. Our approach is to first consider the
linear version of the above ODE, by taking and study its Lyapunov stability.
Exploiting the similarities between linear and nonlinear ODE, we construct a
Lyapunov function for the stability analysis of the given nonlinear differential
equation.