Research Initiation Award: A Unified Framework for Optimal Synthesis in Linear Systems

本研究的目标是完成统一控制 分析和设计方法，包括一维（一个 自变量，通常是时间）和n-d（n个自变量） 系统，用于实现鲁棒性能的降阶控制器 线性的、不确定的工厂模型。 为了得到合成 方法的n-d系统是不是过于保守，我们将 还开发改进的分析技术（验证稳定性， 计算规范等）N-D系统。 这种方法意义重大，因为它将把许多 不同领域的电流控制研究具有统一的理论。 它 将导致算法，将增加控制的作用， 工程师可以在初始系统配置，因为 组件质量和组件建模中的成本/效益权衡 可以先分析。 整个方法是基于线性分式变换 矩阵和一个数学框架来研究它们， 结构奇异值 结构化奇异值是一个 数学工具，用于分析矩阵扰动问题。

The objective of this research is to complete a unified control analysis and design methodology, encompassing both 1-d (one independent variable, usually time) and n-d (n independent variables) systems, for reduced order controllers that achieve robust performance for linear, uncertain plant models. In order to derive synthesis methods for n-d systems which are not overly conservative, we will also develop improved analysis techniques (verifying stability, computing norms, etc.) for n-d systems. This approach is significant, because it will tie together many different areas of current control research with a unified theory. It will lead to algorithms that will increase the role that a control engineer can have in initial system configuration, since the cost/benefit tradeoffs in component quality and in component modelling can be analyzed apriori. The entire methodology is based on linear fractional transformations of matrices and a mathematical framework to study them called the structured singular value. The structured singular value is a mathematical tool useful in analyzing matrix perturbation problems.