Applications of Liapunov Methods in Stability: 245 (Mathematics and Its Applications) - Tapa blanda

Halanay, A.; Rasvan, V.

 
9789401046978: Applications of Liapunov Methods in Stability: 245 (Mathematics and Its Applications)
Tapa blanda
ISBN 10: 9401046972 ISBN 13: 9789401046978
Editorial: Springer, 2012

Sinopsis

The year 1992 marks the centennial anniversary of publication of the celebrated monograph "The General Problem of Stability of Motion" written by A. M. Liapunov. This anniversary inspires to think about the way theory and applications have developed during this century. The first observation one can make is that the so-called "second method", nowadays known as the "Liapunov function method", has received more attention than the "first method"; let us also mention the study of critical cases, which brought more attention recently in connection with the study of bifurcations and with nonlinear stabilization. One of the reasons of popularity of the Liapunov function approach might be the fact that, in many situations in science and engineering, and not only in mechanics, which was the main source of inspiration for the work of Liapunov, natural Liapunov functions may be proposed, intimately connected with the properties of the processes. It is one of the purposes of this book to advocate this idea. From the mathematical viewpoint, the century after the first appear­ ance of Liapunov’s monograph has been characterized both by general­ izations and by refinements of Liapunov’s ideas. But we feel that the most spectacular progress is the understanding of the wide possibilities open for applications by the use of Stability Theory as constructed by Liapunov a century ago. We have tried to show some of the ideas in this direction by start­ ing with our personal experience in the study of some models.

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Reseña del editor

The year 1992 marks the centennial anniversary of publication of the celebrated monograph "The General Problem of Stability of Motion" written by A. M. Liapunov. This anniversary inspires to think about the way theory and applications have developed during this century. The first observation one can make is that the so-called "second method", nowadays known as the "Liapunov function method", has received more attention than the "first method"; let us also mention the study of critical cases, which brought more attention recently in connection with the study of bifurcations and with nonlinear stabilization. One of the reasons of popularity of the Liapunov function approach might be the fact that, in many situations in science and engineering, and not only in mechanics, which was the main source of inspiration for the work of Liapunov, natural Liapunov functions may be proposed, intimately connected with the properties of the processes. It is one of the purposes of this book to advocate this idea. From the mathematical viewpoint, the century after the first appear­ ance of Liapunov's monograph has been characterized both by general­ izations and by refinements of Liapunov's ideas. But we feel that the most spectacular progress is the understanding of the wide possibilities open for applications by the use of Stability Theory as constructed by Liapunov a century ago. We have tried to show some of the ideas in this direction by start­ ing with our personal experience in the study of some models.

Reseña del editor

This volume, which coincides with the centennial anniversary of the publication of the celebrated monograph The General Problem of the Stability Motion by A.M. Liapunov, reviews the current state of the art of the theory and applications of the Liapunov methods.
The book contains an Introduction and four chapters. Chapter 2 presents some general results in stability theory. The remaining chapters deal with applications in power engineering, chemical engineering, and in non-engineering fields such as economics and in the modelling of interacting species. The beauty of the results obtained, the diversity of mathematical tools employed, and the described approach to mathematical modelling provide stimulating considerations for applications in many other fields.
For mathematicians and engineers whose work involves the study and applications of stability theory in systems.

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Editorial
Springer
Año de publicación
2012
Idioma
Inglés
ISBN 10 
9401046972
ISBN 13 
9789401046978
Encuadernación
Tapa blanda
Número de páginas
252
Contacto del fabricante
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Darmstadt
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Alemania

Otras ediciones populares con el mismo título

9780792321200: Applications of Liapunov Methods in Stability: v. 245 (Mathematics and its Applications)

Edición Destacada

ISBN 10:  0792321200 ISBN 13:  9780792321200
Editorial: Springer, 1993
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