Stability Regions of Nonlinear Dynamical Systems

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.