A systematic method to obtain ultimate bounds for perturbed systems
A systematic method to obtain ultimate bounds for perturbed systems
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DOI：
10.1080/00207170600611265
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发表时间：
2007-02
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影响因子：
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通讯作者：
E. Kofman;H. Haimovich;M. Seron
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文献类型：
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作者：
E. Kofman;H. Haimovich;M. Seron
在本文中，我们开发了一个系统的方法来获得连续和离散时间扰动系统的最终界。该方法是基于模态坐标系统的分量分析，从而利用系统的几何形状以及扰动结构，而不需要计算系统的李雅普诺夫函数。该方法被引入线性系统具有恒定分量的扰动界，然后扩展到状态依赖的扰动界的情况下。这种扩展使该方法可以应用于非线性系统，通过处理扰动的非线性系统作为一个线性系统的状态的非线性函数的扰动有界。提供的例子中，所提出的系统的方法产生的界限，更紧密或至少不差于通过标准的李雅普诺夫分析。我们还展示了如何我们的方法可以与李雅普诺夫分析相结合，以提高任何一种方法提供的界限。
In this paper, we develop a systematic method to obtain ultimate bounds for both continuous- and discrete-time perturbed systems. The method is based on a componentwise analysis of the system in modal coordinates and thus exploits the system geometry as well as the perturbation structure without requiring calculation of a Lyapunov function for the system. The method is introduced for linear systems having constant componentwise perturbation bounds and is then extended to the case of state-dependent perturbation bounds. This extension enables the method to be applied to non-linear systems by treating the perturbed non-linear system as a linear system with a perturbation bounded by a non-linear function of the state. Examples are provided where the proposed systematic method yields bounds that are tighter or at least not worse than those obtained via standard Lyapunov analysis. We also show how our method can be combined with Lyapunov analysis to improve on the bounds provided by either approach.