Title

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

Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.

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