Bilinear State Systems on an Unbounded Time Scale

Author

David E. Grow, Missouri University of Science and TechnologyFollow
Nick Wintz

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.

Recommended Citation

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

Department(s)

Mathematics and Statistics

Keywords and Phrases

Bilinear state system; Dynamic equations on time scales; Real analysis on time scales

International Standard Serial Number (ISSN)

0096-3003

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2021 Elsevier, All rights reserved.

Publication Date

15 May 2021