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首页> 外文期刊>IEEE Transactions on Automatic Control >Stability and Performance Analysis for Positive Fractional-Order Systems With Time-Varying Delays
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Stability and Performance Analysis for Positive Fractional-Order Systems With Time-Varying Delays

机译：具有时变时滞的分数阶系统的稳定性和性能分析

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摘要

This paper addresses the stability and L∞-gain analysis problem for continuous-time positive fractional-order delay systems with incommensurate orders between zero and one. A necessary and sufficient condition is firstly given to characterize the positivity of continuous-time fractional-order systems with bounded time-varying delays. Moreover, by exploiting the monotonic and asymptotic property of the constant delay system by virtue of the positivity, and comparing the trajectory of the time-varying delay system with that of the constant delay system, it is proved that the asymptotic stability of positive fractional-order systems is not sensitive to the magnitude of delays. In addition, it is shown that the L∞-gain of a positive fractional-order system is independent of the magnitude of delays and fully determined by the system matrices. Finally, a numerical example is given to show the validity of the theoretical results.
机译：本文讨论了具有零到一之间不等阶的连续时间正分数阶时滞系统的稳定性和L∞增益分析问题。首先给出一个必要的充分条件，以刻画具有时变时滞的连续时间分数阶系统的正性。此外，通过利用正性利用恒定时滞系统的单调和渐近性质，并将时变时滞系统的轨迹与恒定时滞系统的轨迹进行比较，证明了正分数分数阶系统的渐近稳定性。订单系统对延迟的大小不敏感。另外，表明正分数阶系统的L∞增益与时延的大小无关，并且完全由系统矩阵确定。最后，通过数值例子说明了理论结果的正确性。

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