Stability of Dynamical Systems: On the Role of Monotonic and Non-Monotonic Lyapunov Functions
Stability of Dynamical Systems: On the Role of Monotonic and Non-Monotonic Lyapunov Functions
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DOI：
10.1007/978-3-319-15275-2
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发表时间：
2015-03
期刊：
影响因子：
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通讯作者：
A. Michel;Ling Hou;Derong Liu
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文献类型：
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作者：
A. Michel;Ling Hou;Derong Liu
本书的第二版为连续时间和离散时间、有限维和无限维、连续和不连续动力系统所代表的系统模型的分析提供了一个单一的来源。对于这些系统模型，给出了包括涉及单调李雅普诺夫函数的经典李雅普诺夫稳定性理论以及涉及非单调李雅普诺夫函数的相应当代稳定性结果的结果。从几个不同的领域给出了具体的例子，以证明发展的理论适用于许多重要的系统类别，包括数字控制系统，非线性调节系统，脉宽调制反馈控制系统，和人工神经网络。作者涵盖了以下四个一般主题：-上述类型的动力系统的表示和建模-李雅普诺夫和拉格朗日稳定性理论在一般度量空间上定义的涉及单调和非单调李雅普诺夫函数的动力系统的介绍-这种稳定性理论专门化到有限维动力系统-这种稳定性理论专门化到无限维动力系统-充满了例子和要求线性代数，分析和微分方程的基本知识，这本书可以作为在动力系统的稳定性理论研究生课程的教科书。它也可以作为研究生、研究人员和应用数学、工程、计算机科学、经济学、物理和生命科学的实践者的自学参考。第一版的评论：“作者在维护表述的严谨性和为不同类型的系统提供独立语句方面做得非常出色。[这]是一本非常有趣的书，是对现有文献的补充。[它]写得很清楚，用好的例子来说明困难的概念。——alessandro Astolfi， IEEE控制系统杂志，2009年2月
The second edition of this textbook provides a single source for the analysis of system models represented by continuous-time and discrete-time, finite-dimensional and infinite-dimensional, and continuous and discontinuous dynamical systems. For these system models, it presents results which comprise the classical Lyapunov stability theory involving monotonic Lyapunov functions, as well as corresponding contemporary stability results involving non-monotonic Lyapunov functions. Specific examples from several diverse areas are given to demonstrate the applicability of the developed theory to many important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, and artificial neural networks. The authors cover the following four general topics:-Representation and modeling of dynamical systems of the types described above-Presentation of Lyapunov and Lagrange stability theory for dynamical systems defined on general metric spaces involving monotonic and non-monotonic Lyapunov functions-Specialization of this stability theory to finite-dimensional dynamical systems-Specialization of this stability theory to infinite-dimensional dynamical systems Replete with examples and requiring only a basic knowledge of linear algebra, analysis, and differential equations, this book can be used as a textbook for graduate courses in stability theory of dynamical systems. It may also serve as a self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, economics, and the physical and life sciences. Review of the First Edition:“The authors have done an excellent job maintaining the rigor of the presentation, and in providing standalone statements for diverse types of systems.[This] is a very interesting book which complements the existing literature.[It] is clearly written, and difficult concepts are illustrated by means of good examples.”-Alessandro Astolfi, IEEE Control Systems Magazine, February 2009