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Titlebook: Matrix Diagonal Stability in Systems and Computation; Eugenius Kaszkurewicz,Amit Bhaya Book 2000 Springer Science+Business Media New York

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发表于 2025-3-21 17:19:29 | 显示全部楼层 |阅读模式
书目名称Matrix Diagonal Stability in Systems and Computation
编辑Eugenius Kaszkurewicz,Amit Bhaya
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图书封面Titlebook: Matrix Diagonal Stability in Systems and Computation;  Eugenius Kaszkurewicz,Amit Bhaya Book 2000 Springer Science+Business Media New York
描述This monograph presents a collection of results, observations, and examples related to dynamical systems described by linear and nonlinear ordinary differential and difference equations. In particular, dynamical systems that are susceptible to analysis by the Liapunov approach are considered. The naive observation that certain "diagonal-type" Liapunov functions are ubiquitous in the literature attracted the attention of the authors and led to some natural questions. Why does this happen so often? What are the spe­ cial virtues of these functions in this context? Do they occur so frequently merely because they belong to the simplest class of Liapunov functions and are thus more convenient, or are there any more specific reasons? This monograph constitutes the authors‘ synthesis of the work on this subject that has been jointly developed by them, among others, producing and compiling results, properties, and examples for many years, aiming to answer these questions and also to formalize some of the folklore or "cul­ ture" that has grown around diagonal stability and diagonal-type Liapunov functions. A natural answer to these questions would be that the use of diagonal­ type Liapunov
出版日期Book 2000
关键词Matrix; control; control engineering; dynamical systems; dynamische Systeme; matrix computations; neural n
版次1
doihttps://doi.org/10.1007/978-1-4612-1346-8
isbn_softcover978-1-4612-7105-5
isbn_ebook978-1-4612-1346-8
copyrightSpringer Science+Business Media New York 2000
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发表于 2025-3-21 20:54:33 | 显示全部楼层
rdinary differential and difference equations. In particular, dynamical systems that are susceptible to analysis by the Liapunov approach are considered. The naive observation that certain "diagonal-type" Liapunov functions are ubiquitous in the literature attracted the attention of the authors and
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Mathematical Models Admitting Diagonal-Type Liapunov Functions,ss is the quadratic form ..., where . is a positive diagonal matrix and . a real vector. The results are stated in the most general form, without the additional hypotheses or assumptions that arise from the specifics of applications. Material on continuous-and discrete-time systems is classified in different, independent sections.
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Interconnected Systems: Stability and Stabilization,in the area of stability and stabilization of interval systems, introduced in Chapter 3, and of stability of interconnected systems, also known as large scale systems. An application to the stability and stabilization of electrical energy systems is also discussed.
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Diagonally Stable Structures in Systems and Computation,This introductory chapter is devoted to examples that originate from different applications and that illustrate the way in which some special classes of dynamical systems dovetail with the concepts of matrix diagonal stability and the associated diagonal-type Liapunov functions.
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Neural Networks, Circuits, and Systems,This chapter shows and discusses the occurrence of the diagonal structure, introduced in Chapter 1, in several classes of dynamical systems that include neural networks, digital filters, passive RLC circuits, and ecosystems. Some of the examples of Chapter 1, as well as new examples, are treated in greater detail here.
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