Algebraic And Differential Topology Of Robust Stability PDF Download
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Author | : Edmond A. Jonckheere |
Publisher | : Oxford University Press, USA |
Total Pages | : 625 |
Release | : 1997 |
Genre | : Algebraic topology |
ISBN | : 0195093011 |
Download Algebraic and Differential Topology of Robust Stability Book in PDF, ePub and Kindle
In this book, two seemingly unrelated fields - algebraic topology and robust control - are brought together. The book develops algebraic/differential topology proceeding from an easily motivated control engineering problem, showing the relevance of advanced topological concepts and reconstructing the fundamental concepts of algebraic/differential topology from an application-oriented point of view. It is suitable for graduate students in engineering and/or applied mathematics, and academic researchers.
Author | : Edmond A. Jonckheere |
Publisher | : Oxford University Press |
Total Pages | : 625 |
Release | : 1997-05-29 |
Genre | : Mathematics |
ISBN | : 019535768X |
Download Algebraic and Differential Topology of Robust Stability Book in PDF, ePub and Kindle
In this book, two seemingly unrelated fields -- algebraic topology and robust control -- are brought together. The book develops algebraic/differential topology from an application-oriented point of view. The book takes the reader on a path starting from a well-motivated robust stability problem, showing the relevance of the simplicial approximation theorem and how it can be efficiently implemented using computational geometry. The simplicial approximation theorem serves as a primer to more serious topological issues such as the obstruction to extending the Nyquist map, K-theory of robust stabilization, and eventually the differential topology of the Nyquist map, culminating in the explanation of the lack of continuity of the stability margin relative to rounding errors. The book is suitable for graduate students in engineering and/or applied mathematics, academic researchers and governmental laboratories.
Author | : Jean Dieudonné |
Publisher | : Springer Science & Business Media |
Total Pages | : 666 |
Release | : 2009-09-01 |
Genre | : Mathematics |
ISBN | : 0817649077 |
Download A History of Algebraic and Differential Topology, 1900 - 1960 Book in PDF, ePub and Kindle
This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it! —MathSciNet
Author | : Wouter Jongeneel |
Publisher | : Springer Nature |
Total Pages | : 134 |
Release | : 2023-05-16 |
Genre | : Technology & Engineering |
ISBN | : 3031301331 |
Download Topological Obstructions to Stability and Stabilization Book in PDF, ePub and Kindle
This open access book provides a unified overview of topological obstructions to the stability and stabilization of dynamical systems defined on manifolds and an overview that is self-contained and accessible to the control-oriented graduate student. The authors review the interplay between the topology of an attractor, its domain of attraction, and the underlying manifold that is supposed to contain these sets. They present some proofs of known results in order to highlight assumptions and to develop extensions, and they provide new results showcasing the most effective methods to cope with these obstructions to stability and stabilization. Moreover, the book shows how Borsuk’s retraction theory and the index-theoretic methodology of Krasnosel’skii and Zabreiko underlie a large fraction of currently known results. This point of view reveals important open problems, and for that reason, this book is of interest to any researcher in control, dynamical systems, topology, or related fields.
Author | : |
Publisher | : |
Total Pages | : 1060 |
Release | : 1997 |
Genre | : Mechanics, Applied |
ISBN | : |
Download Applied Mechanics Reviews Book in PDF, ePub and Kindle
Author | : C.G. Gibson |
Publisher | : Springer |
Total Pages | : 160 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540379576 |
Download Topological Stability of Smooth Mappings Book in PDF, ePub and Kindle
During the academic year 1974-75, the Department of Pure Mathematics in the University of Liverpool held a seminar on the topological stability of smooth mappings. The main objective was to piece together a complete proof of the topological stability theorem (conjectured by René Thom in 1960, and proved by John Mather in 1970) for which no published accounts existed. This volume comprises a write-up of the seminar by four of the participants. Any mathematician working in this area is conscious of a debt to the inventiveness of Thom, and to Mather for the technical work which placed much that was conjecture on firm mathematical foundations. The proof presented in these notes follows Thom's indications closely, and requires no more than some familiarity with differential topology and commutative algebra of the reader.
Author | : Keqin Gu |
Publisher | : Springer Science & Business Media |
Total Pages | : 367 |
Release | : 2012-12-06 |
Genre | : Technology & Engineering |
ISBN | : 1461200393 |
Download Stability of Time-Delay Systems Book in PDF, ePub and Kindle
This book is a self-contained presentation of the background and progress of the study of time-delay systems, a subject with broad applications to a number of areas.
Author | : R. Bott |
Publisher | : Springer |
Total Pages | : 183 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 354037616X |
Download Lectures on Algebraic and Differential Topology Book in PDF, ePub and Kindle
Author | : |
Publisher | : |
Total Pages | : 1524 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : |
Download Mathematical Reviews Book in PDF, ePub and Kindle
Author | : R.V. Gamkrelidze |
Publisher | : Routledge |
Total Pages | : 252 |
Release | : 2022-01-27 |
Genre | : Mathematics |
ISBN | : 1351467549 |
Download Algebraic and Differential Topology Book in PDF, ePub and Kindle
Algebraic and Differential Topology presents in a clear, concise, and detailed manner the fundamentals of homology theory. It first defines the concept of a complex and its Betti groups, then discusses the topolgoical invariance of a Betti group. The book next presents various applications of homology theory, such as mapping of polyhedrons onto other polyhedrons as well as onto themselves. The third volume in L.S. Pontryagin's Selected Works, this book provides as many insights into algebraic topology for today's mathematician as it did when the author was making his initial endeavors into this field.