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

本研究涉及一个基本工具，称为快速提升，它在使用数字设备或涉及材料、信息、能量等传输的控制系统的综合和分析的高级处理中发挥着重要作用。本研究从算子理论的角度对该工具进行数学处理，并进一步研究简化思想的扩展，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.