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Bilinear state systems on an unbounded time scale

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  • Grow, David
  • Wintz, Nick

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.

Suggested Citation

  • Grow, David & Wintz, Nick, 2021. "Bilinear state systems on an unbounded time scale," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    • Handle: RePEc:eee:apmaco:v:397:y:2021:i:c:s0096300320308705
    DOI: 10.1016/j.amc.2020.125917
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    References listed on IDEAS

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    1. U. Ledzewicz & H. Schättler, 2002. "Optimal Bang-Bang Controls for a Two-Compartment Model in Cancer Chemotherapy," Journal of Optimization Theory and Applications, Springer, vol. 114(3), pages 609-637, September.
    2. Zaidong Zhan & W. Wei, 2009. "Necessary Conditions for a Class of Optimal Control Problems on Time Scales," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-14, June.
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