l-Delay Input and Initial-State Reconstruction for Discrete-Time Linear Systems
l-Delay Input and Initial-State Reconstruction for Discrete-Time Linear Systems
复制标题
离散时间线性系统的 l 延迟输入和初始状态重建
DOI：
10.1007/s00034-010-9214-4
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
D. Bernstein
中科院分区：
文献类型：
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作者：
S. Kirtikar;H. Palanthandalam;E. Zattoni;D. Bernstein
通过定义l-延迟输入和初始状态能观性，推广了多输入多输出离散线性系统输入重构的已有结果。这个属性为重建未知输入和未知初始条件提供了基础，因此是比l-延迟左可逆性更强的概念，l-延迟左可逆性仅在初始状态已知时才允许输入重建。这些性质通过主要结果（定理4）联系起来，该结果指出，具有至少与输入一样多的输出的MIMO离散时间线性系统是l-延迟输入和初始状态可观测的当且仅当它是l-延迟左可逆的并且没有不变零点。此外，我们证明了输入和状态重建的最小延迟是相同的左可逆的最小延迟。当传输零点存在时，我们数值演示了l-延迟输入和状态重构，以显示输入重构误差如何取决于零点的位置。具体而言，最小相位零点引起衰减的输入重构误差，非最小相位零点引起增长的重构误差，并且单位圆上的零点引起持续的重构误差。
Prior results on input reconstruction for multi-input, multi-output discrete-time linear systems are extended by defining l-delay input and initial-state observability. This property provides the foundation for reconstructing both unknown inputs and unknown initial conditions, and thus is a stronger notion than l-delay left invertibility, which allows input reconstruction only when the initial state is known. These properties are linked by the main result (Theorem 4), which states that a MIMO discrete-time linear system with at least as many outputs as inputs is l-delay input and initial-state observable if and only if it is l-delay left invertible and has no invariant zeros. In addition, we prove that the minimal delay for input and state reconstruction is identical to the minimal delay for left invertibility. When transmission zeros are present, we numerically demonstrate l-delay input and state reconstruction to show how the input-reconstruction error depends on the locations of the zeros. Specifically, minimum-phase zeros give rise to decaying input reconstruction error, nonminimum-phase zeros give rise to growing reconstruction error, and zeros on the unit circle give rise to persistent reconstruction error.