Abstract
An explicit criterion for positivity of the solution semigroup of linear Volterra integro-differential systems with infinitely many delays is given. Then exponential asymptotic stability is studied, and it is shown that, roughly speaking, a linear Volterra integro-differential system with delay is exponentially asymptotically stable if its characteristic equation has no zeros in the closed right half complex plane and the “kernel part” of the system exponentially decays. In particular, some simple criteria for exponential asymptotic stability of positive systems are presented. Finally, two sufficient conditions for exponential asymptotic stability of positive systems subjected to structured perturbations and affine perturbations are given. A simple example is given to illustrate the obtained results.
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.
