Stability Regions of Nonlinear Dynamical Systems

Hsiao-Dong Chiang is Professor of Electrical and Computer Engineering at Cornell University, New York, President of Bigwood Systems, Inc. (BSI), Ithaca, New York and President of Global Optimal Technology, Inc. (GOTI). He is a Fellow of the IEEE. Luís F. C. Alberto is an Associate Professor at the Electrical Engineering Department of the School of Engineering of Sao Carlos, University of São Paulo and a director of the SBA (Brazilian Society of Automation) 2013–14.

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.