Applications of Liapunov methods in stability /
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| Author / Creator: | Halanay, Aristide |
|---|---|
| Imprint: | Dordrecht ; Boston : Kluwer Academic Publishers, c1993. |
| Description: | x, 237 p. : ill. ; 25 cm. |
| Language: | English |
| Series: | Mathematics and its applications ; v. 245 Mathematics and its applications (Kluwer Academic Publishers) v. 245. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/1473537 |
Table of Contents:
- 1. Introduction
- 2. Some General Results in Stability Theory. 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
- 3. Stability Problems in Power Engineering. 3.1. Stability of Synchronous Generators. Mathematical Models of Synchronous Machine. Liapunov Functions Associated with Synchronous Machines. Inherent Stability of Synchronous Machines. Stability of the Synchronous Machine with Prime Mover and Speed Governor. The Domain of Admissible Manoeuvres. The Reduction Principle and Global behaviour of the Synchronous Generator with Prime Mover and Speed Governor. 3.2. Stabilization of Class of Steam Turbines for Heat-Electricity Generation. Configurations and Mathematical Models. The Invariant Set of the Models. Steady-States. Systems in Deviations and Inherent Stability. Stabilization. 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
- 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. The Mathematical Model. Equilibrium Points. The Liapunov Function and its Properties. Stability Results and Qualitative Properties. 4.3. Processes in Plate Columns. 4.3.1. The Invariant Set of the Model. Steady State Solutions. Stability of Steady State
- 5. Stability Problems in Non-Engineering Fields. 5.1. Stability of Competitive Equilibrium in Walrasian Economic Model. The Model. Properties of the Model. Stability. 5.2. Volterra Models of Interacting Species. Other Properties of Dissipative Communities. A Simple Model with Harvesting. Appendix 1. Existence of Equilibria in Walrasian Economic Model.
