Bilinear state systems on an unbounded time scale
Document Type
Article
Publication Title
Applied Mathematics and Computation
Abstract
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.
DOI
https://doi.org/10.1016/j.amc.2020.125917
Publication Date
5-15-2021
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Grow, David and Wintz, Nick, "Bilinear state systems on an unbounded time scale" (2021). Faculty Scholarship. 20.
https://digitalcommons.lindenwood.edu/faculty-research-papers/20
