Operator-Theoretic Study on the Synthesis and Analysis of Control Systems via Fast-Lifting and Its Algebraic Extension

这项研究涉及一种名为快速提升的基本工具，在使用数字设备或涉及材料、信息、能量等运输的控制系统的综合和分析中，它在高级处理中发挥着重要作用。它从算子论的角度对这一工具进行了数学处理，并进一步研究了简化思想的扩展，以便它们可以应用于其他类型的控制系统。

The study dealt with a basic tool called fast-lifting that plays a significant role in advanced treatment in the synthesis and analysis of control systems employing digital devices or involving transportation of material, information, energy and so on. It mathematically tackles this tool from an operator-theoretic viewpoint, and further studies extensions of simplified ideas so that they can be applied to other types of control systems.