Applications of Liapunov Methods in Stability

Softcover Nachdruck of the original 1. Auflage 1993
ISBN: 978-94-010-4697-8
Verlag: Springer Netherlands

Buch, Englisch, Band 245, 237 Seiten, Format (B × H): 160 mm x 240 mm, Gewicht: 409 g

Reihe: Mathematics and Its Applications

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.

Zielgruppe

Research

Autoren/Hrsg.

Rasvan, V.

Halanay, A.

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Technische Wissenschaften Verfahrenstechnik | Chemieingenieurwesen | Biotechnologie Verfahrenstechnik, Chemieingenieurwesen
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau

Inhaltsverzeichnis

1 Introduction.- References.- 2 Some General Results in Stability Theory.- 2.1 Basic Concepts.- 2.2 Linear Systems with Constant Coefficients. Stability by the First Approximation.- 2.3 Liapunov Functions.- 2.4 Application of Liapunov Functions in Some Problems of Hydraulic Engineering.- References.- 3 Stability Problems in Power Engineering.- 3.1 Stability of Synchronous Generators. Mathematical Models of Synchronous Machine.- 3.2 Stabilization of Class of Steam Turbines for Heat-Electricity Generation.- Appendix 1. The Theorem of G.A. Leonov.- Appendix 2. A Second Order Equation.- Appendix 3. Liapunov Equations.- Appendix 4. The Yakubovich — Kalman — Popov Lemma.- Appendix 5. A Result Concerning Exponential Stability.- References.- 4 Stability Problems in Chemical Engineering.- 4.1 First Model in Chemical Kinetics.- 4.2 Stability of Closed Chemical System Subject to Mass — Action Law.- 4.3 Processes in Plate Columns.- References.- 5 Stability Problems in Non — Engineering Fields.- 5.1 Stability of Competitive Equilibrium in Walrasian Economic Model.- 5.2 Volterra Models of Interacting Species.- Appendix 1. Existence of Equilibria in Walrasian Economic Model.- Appendix 2.- References.