Applications of Liapunov Methods in Stability Vol. 245 : Mathematics and Its Applications

By: A. Halanay, V. Rasvan

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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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Preface
About the Notations
Introduction	p. 1
Some General Results in Stability Theory	p. 15
Linear Systems with Constant Coefficients. Stability by the First Approximation	p. 17
Liapunov Functions	p. 23
Application of Liapunov Functions in Some Problems of Hydraulic Engineering	p. 35
Stability Problems in Power Engineering	p. 61
Stability of Synchronous Generators. Mathematical Models of Synchronous Machine	p. 61
Liapunov Functions Associated with Synchronous Machines	p. 68
Inherent Stability of Synchronous Machines	p. 71
Stability of the Synchronous Machine with Prime Mover and Speed Governor	p. 74
The Domain of Admissible Manoeuvres	p. 78
The Reduction Principle and Global behaviour of the Synchronous Generator with Prime Mover and Speed Governor	p. 80
Stabilization of Class of Steam Turbines for Heat-Electricity Generation	p. 85
Configurations and Mathematical Models	p. 86
The Invariant Set of the Models	p. 87
Steady-States	p. 89
Systems in Deviations and Inherent Stability	p. 91
Stabilization	p. 93
Appendix 1. The Theorem of G.A. Leonov	p. 101
Appendix 2. A Second Order Equation	p. 106
Appendix 3. Liapunov Equations	p. 111
Appendix 4. The Yakubovich - Kalman - Popov Lemma	p. 113
Appendix 5. A Result Concerning Exponential Stability	p. 117
Stability Problems in Chemical Engineering	p. 125
First Model in Chemical Kinetics	p. 125
Stability of Closed Chemical System Subject to Mass-Action Law	p. 131
The Mathematical Model	p. 131
Equilibrium Points	p. 138
The Liapunov Function and its Properties	p. 143
Stability Results and Qualitative Properties	p. 148
Processes in Plate Columns	p. 153
The Invariant Set of the Model	p. 160
Steady State Solutions	p. 163
Stability of Steady State	p. 173
Stability Problems in Non-Engineering Fields	p. 191
Stability of Competitive Equilibrium in Walrasian Economic Model	p. 191
The Model	p. 191
Properties of the Model	p. 193
Stability	p. 203
Volterra Models of Interacting Species	p. 205
Other Properties of Dissipative Communities	p. 212
A Simple Model with Harvesting	p. 216
Appendix 1. Existence of Equilibria in Walrasian Economic Model	p. 222
Index	p. 235
Table of Contents provided by Blackwell. All Rights Reserved.

Applications of Liapunov Methods in Stability Vol. 245 : Mathematics and Its Applications

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