New Theory for Sampled-Data Control Systems and Its Applications

本研究项目旨在系统地研究由首席研究员发展的现代函数论方法对采样数据控制系统的影响。这里的重点是基于称为提升的新概念的设计模型中的内置样本间行为，因此与经典上下文有很大的不同。主要内容包括：1.频域分析/综合方法；2.频率响应的介绍与计算；3.H^*设计方法；4.这些计算问题的算法。在研究期间，我们成功地取得了以下成果：1.介绍了采样数据系统频率响应的新概念，2.与脉冲调制公式的关系，3.它的有限维特征值问题的表征，4.H^*优化问题的解，5.各种计算算法，6.作为CAD软件包实现。目前的研究与这一主题的相互作用无疑是未来最合乎逻辑、最相关、可能也是最富有成果的目标。

The present research project intends to give a systematic study of the modern function theoretic approach, developed by the principal investigator, to sampled-data control systems. The emphasis here is upon the built-in intersample behavior in the design model based on the new notion called lifting, thereby differing greatly from the classical context. It aims at advancing1.frequency domain analysis/synthesis methods,2.introduction and introduction and computation of frequency response,3.H^* design methods4.algorithms for these computational issues.During the research term, we have successfully obtained the following results :1.introduction of the new notion of frequency response for sampled-data systems,2.relationship with the impulse modulation formula,3.its characterization via finite-dimensional eigenvalue problem,4.a solution to the H^* optimization problem,5.various computational algorithms,6.implementation as a CAD package.A promising sign of application toward signal processing has also been obtained. The interplay of the present research with this theme is undoubtedly the most logical, related and perhaps most fruitful target for the future.