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.

中文翻译：

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无界时间尺度上的双线性状态系统

我们证明了在无界时间尺度上具有局部本质界系数的双线性状态系统解的存在性和唯一性。我们为这些解决方案获得了Volterra级数表示，它在时间尺度的紧凑子集上是标准收敛的和一致收敛的。我们证明相关的状态转移矩阵具有相似的会聚Peano-Baker级数表示，并为其可逆性确定了必要和充分的条件。最后，我们为动态双线性系统提供了数值应用程序-调频信号模型和两室癌症化疗模型。