Stability Regions of Nonlinear Dynamical Systems
Theory, Estimation, and Applications

An authoritative treatment by leading researchers covering theory and optimal estimation, along with practical applications.

Hsiao-Dong Chiang (Author), Luís F. C. Alberto (Author)

9781107035409, Cambridge University Press

Hardback, published 13 August 2015

484 pages, 172 b/w illus. 16 tables
24.4 x 17 x 2.7 cm, 1.08 kg

This book offers a comprehensive exposition of the theory, estimation methods, and applications of stability regions and stability boundaries for nonlinear dynamical systems. … All the proofs are given in a rigorous manner and various examples are presented for illustration. The book is written concisely and will provide very useful guidance for researchers and graduate students who are interested in dynamical systems and their applications.' Vu Hoang Linh, Mathematical Reviews

This authoritative treatment covers theory, optimal estimation and a range of practical applications. The first book on the subject, and written by leading researchers, this clear and rigorous work presents a comprehensive theory for both the stability boundary and the stability regions of a range of nonlinear dynamical systems including continuous, discrete, complex, two-time-scale and non-hyperbolic systems, illustrated with numerical examples. The authors also propose new concepts of quasi-stability region and of relevant stability regions and their complete characterisations. Optimal schemes for estimating stability regions of general nonlinear dynamical systems are also covered, and finally the authors describe and explain how the theory is applied in applications including direct methods for power system transient stability analysis, nonlinear optimisation for finding a set of high-quality optimal solutions, stabilisation of nonlinear systems, ecosystem dynamics, and immunisation problems.

1. Introduction
Part I. Theory: 2. Stability, limit sets and stability regions
3. Energy function theory
4. Stability regions of continuous dynamical systems
5. Stability regions of attracting sets of complex nonlinear dynamical systems
6. Quasi-stability regions of continuous dynamical systems - theory
7. Stability regions of constrained dynamical systems
8. Relevant stability boundary of continuous dynamical systems
9. Stability regions of discrete dynamical systems
Part II. Estimation: 10. Estimating stability regions of continuous dynamical systems
11. Estimating stability regions of complex continuous dynamical systems
12. Estimating stability regions of discrete dynamical systems
13. A constructive methodology to estimate stability regions of nonlinear dynamical systems
14. Estimation of relevant stability regions
15. Critical evaluation of numerical methods for approximating stability boundaries
Part III. Advanced Topics: 16. Stability regions of two-time scale continuous dynamical systems
17. Stability regions for a class of non-hyperbolic dynamical systems - theory and estimation
18. Optimal estimation of stability regions for a class of large-scale nonlinear dynamic systems
19. Bifurcations of stability regions
Part IV. Applications: 20. Application of stability regions to direct stability analysis of large-scale electric power systems
21. Stability-region-based methods for multiple optimal solutions of nonlinear programming
22. Perspectives and future directions.

Subject Areas: Automatic control engineering [TJFM], Maths for engineers [TBJ], Engineering: general [TBC], Optimization [PBU]