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On Asymptotic Stability of Discrete-Time Linear Time-Varying Systems

机译：离散线性时变系统的渐近稳定性

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This note is concerned with asymptotic stability analysis of discrete-time linear time-varying (DLTV) systems. The contribution can be summarized as follows. First, the difference between nonuniformly exponential stability (ES), which was not well recognized in the literature, and uniformly ES (UES) was revealed and illustrated by numerical examples. Second, some state transition matrices and difference Lyapunov inequalities (DLIs) based necessary and sufficient conditions were derived for testing different stability concepts including asymptotic stability (AS), ES, and UES of general DLTV systems. The main feature of the DLIs-based criteria is that the time-difference of the Lyapunov function is not required to be negative definite. Finally, the ES concept was utilized for analysis stability of a class of upper triangular DLTV systems and perturbated DLTV systems. The effectiveness of the proposed results was demonstrated by some examples.
机译：本说明与离散时间线性时变（DLTV）系统的渐近稳定性分析有关。贡献可总结如下。首先，通过数值示例揭示并说明了非均匀指数稳定性（ES）和均匀ES（UES）之间的差异，该差异在文献中未得到很好的认识。其次，推导了一些状态转换矩阵和基于李雅普诺夫不等式（DLI）的必要条件和充分条件，以测试常规DLTV系统的不同稳定性概念，包括渐近稳定性（AS），ES和UES。基于DLI的标准的主要特征是Lyapunov函数的时间差不需要为负定。最后，ES概念被用于分析一类上三角DLTV系统和扰动DLTV系统的稳定性。一些实例证明了所提出结果的有效性。

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