Bilinear State Systems on an Unbounded Time Scale
We demonstrate the existence and uniqueness of solutions to a bilinear state system with locally essentially bounded coefficients on an unbounded time scale. We obtain a Volterra series representation for these solutions which is norm convergent and uniformly convergent on compact subsets of the time scale. We show the associated state transition matrix has a similarly convergent Peano-Baker series representation and identify a necessary and sufficient condition for its invertibility. Finally, we offer numerical applications for dynamic bilinear systems - a frequency modulated signal model and a two-compartment cancer chemotherapy model.
D. E. Grow and N. Wintz, "Bilinear State Systems on an Unbounded Time Scale," Applied Mathematics and Computation, vol. 397, Elsevier, May 2021.
The definitive version is available at https://doi.org/10.1016/j.amc.2020.125917
Mathematics and Statistics
Keywords and Phrases
Bilinear state system; Dynamic equations on time scales; Real analysis on time scales
International Standard Serial Number (ISSN)
Article - Journal
© 2021 Elsevier, All rights reserved.
15 May 2021