Recent results have shown that, for continuous-time systems obtained by cascading an asymptotically stable system with an inner system, the first $n$ Hankel singular values are greater than or equal to those of the original system. Similarly, cascading a system in minimal form with an inner system, the same property holds for the linear quadratic Gaussian (LQG) characteristic values. In this article, we consider the discrete-time case and demonstrate that the property also holds for these systems. A very important consequence stemming from these results is that the Hankel singular values and the LQG characteristic values of input-delayed discrete systems are greater than or equal to those of their zero-delay counterpart.

中文翻译：

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与内系统级联的离散时间线性系统的Hankel奇异值和LQG特征值

最近的结果表明，对于通过将渐近稳定系统与内部系统级联获得的连续时间系统，前 $n$ Hankel 奇异值大于或等于原始系统的奇异值。类似地，将最小形式的系统与内部系统级联，线性二次高斯 (LQG) 特征值具有相同的属性。在本文中，我们考虑离散时间情况并证明该性质也适用于这些系统。从这些结果中得出的一个非常重要的结论是输入延迟离散系统的 Hankel 奇异值和 LQG 特征值大于或等于它们的零延迟对应系统的奇异值和 LQG 特征值。