Abstract This paper investigates the stability and L ∞ -gain problems of positive linear systems with bounded time-varying delays on time scales. For such systems on time scales, the positivity conditions are firstly established. Then, in virtue of the monotonic and asymptotic properties of a positive linear system with the specified time delay, the stability condition is presented for positive systems with bounded time-varying delays on time scales, which is independent of the delay magnitude and time scale. Furthermore, we prove that the L ∞ -gain of such systems is also independent of both the magnitude of delays and time scale, which can be fully determined by system matrices. Finally, two numerical examples are presented to show the validity of the obtained results.

中文翻译：

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在时间尺度上具有有界时变延迟的正系统的稳定性和 L∞ 性能分析

摘要 本文研究了时间尺度上具有有界时变延迟的正线性系统的稳定性和L ∞ -增益问题。对于时间尺度上的此类系统，首先建立正性条件。然后，利用具有指定时滞的正线性系统的单调和渐近特性，给出了时标上时变有界时滞正系统的稳定性条件，该稳定性条件与时滞幅度和时标无关。此外，我们证明了这种系统的 L ∞ -增益也与延迟的大小和时间尺度无关，这可以完全由系统矩阵确定。最后，给出了两个数值例子来说明所得结果的有效性。