Abstract
In this paper we present a new dual approach to investigating the stability of the system of two nonautonomous ODE with the right-hand side being only Lebesgue measurable with respect to time t. We define a new dual Lapunov function S which depends on three variables, and we give sufficient conditions for finite and fixed-time stability for the system using a dual Hamilton-Jacobi inequality and taking advantage of a class of functions M and MB. This method allows simultaneous investigation of the finite and fixed-time stability of the primary and the dual equation. We give some examples to illustrate the results obtained. As an application of this dual approach, we define the region of attraction and illustrate with an example.
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.
