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Dynamic stabilization of regular linear systems

机译：规则线性系统的动态稳定

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摘要

We consider a general class of infinite-dimensional linear systems, called regular linear systems, for which convenient representations are known to exist both in time and in frequency domain. For this class of systems, we investigate the concepts of stabilizability and detectability, in particular, their invariance under feedback and their relationship to exponential stability. We introduce two concepts of dynamic stabilization, the first formulated as usual, with the plant and the controller connected in feedback, and the second with two feedback loops. Even for finite-dimensional systems, the second concept, stabilization with an internal loop in the controller, is more general. We argue that the more general concept is the natural one, and we derive sufficient conditions under which an observer-based stabilizing controller with an internal loop can be constructed
机译：我们考虑一类普通的无穷维线性系统，称为规则线性系统，已知方便的表示形式在时域和频域中都存在。对于此类系统，我们研究了稳定性和可检测性的概念，尤其是它们在反馈下的不变性以及它们与指数稳定性的关系。我们介绍了动态稳定的两个概念，第一个是照常制定的，将设备和控制器以反馈方式连接，第二个是两个反馈回路。即使对于有限维系统，第二个概念，即控制器内部回路的稳定化，也更为普遍。我们认为，更一般的概念是自然的概念，并且我们得出了足够的条件，可以在此条件下构造具有内部回路的基于观察者的稳定控制器

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