Title

Bilinear State Systems on an Unbounded Time Scale

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.

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

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