绝对稳定性导致无限维度

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-08-08 DOI:10.1098/rspa.2003.1261

R. Curtain, H. Logemann, O. Staffans

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引用次数: 20

摘要

我们得到了无限维系统在输入输出条件下的波波夫和圆准则型的绝对稳定性结果。我们的结果适用于反馈系统，其中线性部分是输入输出稳定线性系统和积分器的串联互连，非线性满足扇形条件，特别是允许饱和和死区效应。我们使用开发的输入-输出理论来推导绝对稳定性的状态空间结果，应用于反馈系统，其中线性部分是指数稳定的，适定的无限维系统和积分器的串联互连。

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Absolute-stability results in infinite dimensions

We derive absolute–stability results of Popov and circle–criterion type for infinite–dimensional systems in an input–output setting. Our results apply to feedback systems in which the linear part is the series interconnection of an input–output stable linear system and an integrator, and the nonlinearity satisfies a sector condition which, in particular, allows for saturation and deadzone effects. We use the input–output theory developed to derive state–space results on absolute stability applying to feedback systems in which the linear part is the series interconnection of an exponentially stable, well–posed infinite–dimensional system and an integrator.

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来源期刊

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences

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期刊介绍： Proceedings A publishes articles across the chemical, computational, Earth, engineering, mathematical, and physical sciences. The articles published are high-quality, original, fundamental articles of interest to a wide range of scientists, and often have long citation half-lives. As well as established disciplines, we encourage emerging and interdisciplinary areas.