We study the problem of arbitrary eigenvalue spectrum assignment for a linear discrete-time control system with delays defined by a linear difference equation of the $n$th order with multiple inputs and multiple outputs via static output feedback with delays. Necessary and sufficient conditions are obtained for arbitrary eigenvalue spectrum assignment by linear static output feedback with delays. These conditions are expressed in terms of system coefficients. A corollary on stabilization is derived. An illustrative example is presented.

中文翻译：

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具有状态变量延迟的线性差分方程的静态输出反馈的频谱分配和稳定

我们研究了线性离散时间控制系统的任意特征值谱分配问题，该系统具有由线性差分方程定义的延迟 $n$通过带延迟的静态输出反馈实现多输入多输出的阶次。通过具有延迟的线性静态输出反馈，获得了任意特征值谱分配的充要条件。这些条件用系统系数表示。推导出稳定性的一个推论。给出了一个说明性示例。