Bilinear state systems on an unbounded time scale

David Grow and Nick Wintz

Applied Mathematics and Computation, 2021, vol. 397, issue C

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.

Keywords: Bilinear state system; Dynamic equations on time scales; Real analysis on time scales (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:397:y:2021:i:c:s0096300320308705

DOI: 10.1016/j.amc.2020.125917

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