Input to State Stability: Basic Concepts and Results
Input to State Stability: Basic Concepts and Results
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DOI：
10.1007/978-3-540-77653-6_3
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发表时间：
2008
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通讯作者：
Eduardo Sontag
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文献类型：
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作者：
Eduardo Sontag
非线性反馈系统的分析和设计最近经历了异常丰富的进步和成熟期，这在很大程度上受到以下因素的推动：（1）某些基本概念的发现，以及（2）系统分类方法的识别，对于这些系统，系统分解方法可以产生有效且易于计算的控制定律。这两个方面是互补的，因为后一种方法通常基于对组合下前一个系统属性的有效性的归纳验证（在[62]中使用的术语中，理论概念的“激活”导致“建设性”控制）。这个说明性演示解决了第一个方面，特别是关于干扰的鲁棒性问题的精确表述，在 国家稳定的输入范式。我们提供主要概念的直观和非正式的演示。更精确的陈述，尤其是关于较早结果的陈述，在引用的论文以及之前的几项调查中给出，例如[103, 105]（其中本文代表了更新），但我们提供了有关相对较新的工作的更多细节。关于基本框架的应用和扩展，我们给出了一些文献的指导，但我们不关注反馈设计和具体的工程问题；对于后者，我们建议读者参考[27,43,44,58,60,66,96]等教科书。
The analysis and design of nonlinear feedback systems has recently undergone an exceptionally rich period of progress and maturation, fueled, to a great extent, by (1) the discovery of certain basic conceptual notions, and (2) the identification of classes of systems for which systematic decomposition approaches can result in effective and easily computable control laws. These two aspects are complementary, since the latter approaches are, typically, based upon the inductive verification of the validity of the former system properties under compositions (in the terminology used in [62], the “activation” of theoretical concepts leads to “constructive” control).This expository presentation addresses the first of these aspects, and in particular the precise formulation of questions of robustness with respect to disturbances, formulated in the paradigm ofinput to state stability. We provide an intuitive and informal presentation of the main concepts. More precise statements, especially about older results, are given in the cited papers, as well as in several previous surveys such as [103, 105] (of which the present paper represents an update), but we provide a little more detail about relatively recent work. Regarding applications and extensions of the basic framework, we give some pointers to the literature, but we do not focus on feedback design and specific engineering problems; for the latter we refer the reader to textbooks such as [27, 43, 44, 58, 60, 66, 96].