Mathematical Sciences: Algebraic Methods in Systems Theory

数学科学：系统论中的代数方法

• 批准号: 9400965
• 负责人: Joachim Rosenthal
• 金额: $ 6万
• 依托单位: University of Notre Dame
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 1997-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9400965&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algebraic; Methods; Systems

9300805 Rosenthal This project addresses a number of issues in systems theory, interpolation theory and coding theory, all of which involve algebraic properties of the class of all autoregressive systems of a bounded degree. The main objectives of the research are improved methods for the design of stabilizing dynamic feedback compensators, a better understanding of the interplay between issues of robustness and topological properties of the space of transfer functions, and new methods for constructing classes of convolutional codes with a low complexity and a large free distance. Many real world systems may be mathematically modeled by so- called linear systems. Two examples of a linear system are dynamic feedback compensators, which are widely used in the design of feedback controllers, and convolutional encoders and decoders, which are implemented in many data transmission schemes. It is the goal of this project to develop a mathematical theory which will lead to improved design techniques for feedback controllers of various types as well as more efficient convolutional encoders and decoders. ***

小行星9300805 这个项目解决了一些问题，在系统理论，插值理论和编码理论，所有这些都涉及代数性质的类的所有自回归系统的一个有界度。研究的主要目标是改进方法的稳定动态反馈补偿器的设计，更好地了解的鲁棒性和拓扑性质的空间的传递函数的问题之间的相互作用，和新的方法构建类卷积码具有低复杂性和大的自由距离。 许多真实的世界系统可以用所谓的线性系统来数学建模。线性系统的两个例子是动态反馈补偿器和卷积编码器和解码器，动态反馈补偿器广泛用于反馈控制器的设计，卷积编码器和解码器在许多数据传输方案中实现。这个项目的目标是开发一种数学理论，这将导致各种类型的反馈控制器以及更有效的卷积编码器和解码器的改进设计技术。 ***