Abstract
The goal of this paper is twofold. The first part presents a converse Lyapunov theorem for the notion of uniform practical exponential stability of nonlinear differential equations in presence of small perturbation. This class of nonlinear differential equations can be viewed as parametric differential equations. The second part provides the classical perturbation method of seeking an approximate solution as a finite Taylor expansion of the exact solution. The practical asymptotic validity on the approximate is established on infinite-time interval. Finally, we give a numerical example to prove the validity of our methods.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
