Wellposedness and stabilization of a class of infinite dimensional bilinear control systems

J. Daafouz, M. Tucsnak, J. Valein
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引用次数: 2

Abstract

We consider a class of infinite dimensional systems involving a control function u taking values in [0; 1]. This class contains, in particular, the average models of some infinite dimensional switched systems. We prove that the system is well-posed and obtain some regularity properties. Moreover, when u is given in an appropriate feedback form and the system satisfies appropriate observability assumptions, we show that the system is weakly stable. The main example concerns the analysis and stabilization of a model of Boost converter connected to a load via a transmission line. The main novelty consists in the fact that we give a rigorous wellposedness and stability analysis of coupled systems, in the presence of duty cycles.
一类无限维双线性控制系统的适定性与镇定性
考虑一类无限维系统,其控制函数u取值范围为[0;1]。特别地,这类包含了一些无限维切换系统的平均模型。证明了该系统是适定的,并得到了一些正则性。此外,当u以适当的反馈形式给出且系统满足适当的可观测性假设时,我们证明了系统是弱稳定的。主要的例子是通过传输线连接到负载的升压变换器模型的分析和稳定。主要的新颖之处在于我们给出了耦合系统在占空比下的严格的适位性和稳定性分析。
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