Stability analysis of linear delay systems with cone invariance
Stability analysis of linear delay systems with cone invariance
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DOI：
10.1016/j.automatica.2014.12.014
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发表时间：
2015-03
期刊：
影响因子：
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通讯作者：
Jun Shen;W. Zheng
中科院分区：
文献类型：
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作者：
Jun Shen;W. Zheng
本文研究具有锥不变性的线性时滞系统的稳定性和输入输出增益分析。基于锥上的偏序，研究了常时滞保锥系统轨线的单调性。然后，通过比较常时滞系统和时变时滞系统的轨迹，证明了具有区间时变时滞的锥保持系统是渐近稳定的当且仅当相应的无时滞系统是渐近稳定的.这意味着锥保持系统的稳定性对时滞的大小不敏感。此外，基于锥诱导范数，给出了输入输出锥保持系统锥诱导增益的一个系统矩阵的显式刻画。最后，数值例子来说明理论结果。
This paper is concerned with the stability and input–output gain analysis of linear delay systems with cone invariance. Based on the partial ordering over a cone, the monotonicity of the trajectory of the cone-preserving systems with constant delays is first studied. Then, by comparing the trajectory of the constant delay systems and that of time-varying delay systems, we prove that a cone-preserving system with interval time-varying delays is asymptotically stable if and only if the corresponding delay-free system is asymptotically stable. This implies that the stability of a cone-preserving system is insensitive to the magnitude of the delays. Moreover, based on the cone-induced norms, an explicit characterization on the cone-induced gain of an input–output cone-preserving system is given in terms of system matrices. Finally, numerical examples are provided to illustrate the theoretical results.