Stability regions of nonlinear dynamical systems: theory, estimation, and applications
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 o...
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| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2015
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| Subjects: | |
| Online Access: | BSB01 FHN01 TUM01 Volltext |
| Summary: | 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 |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 Online-Ressource (X, 472 Seiten) |
| ISBN: | 9781139548861 |
| DOI: | 10.1017/CBO9781139548861 |
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| 505 | 8 | |a 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; 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 | |
| 520 | |a 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 | ||
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Record in the Search Index
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| any_adam_object | |
| author | Chiang, Hsiao-Dong Alberto, Luís F. C. |
| author_GND | (DE-588)1079181261 |
| author_facet | Chiang, Hsiao-Dong Alberto, Luís F. C. |
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| contents | 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; 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 |
| ctrlnum | (ZDB-20-CBO)CR9781139548861 (OCoLC)930541033 (DE-599)BVBBV043940190 |
| dewey-full | 003/.85 003.85 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 003 - Systems |
| dewey-raw | 003/.85 003.85 |
| dewey-search | 003/.85 003.85 |
| dewey-sort | 13 285 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| doi_str_mv | 10.1017/CBO9781139548861 |
| format | Electronic eBook |
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| id | DE-604.BV043940190 |
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| isbn | 9781139548861 |
| language | English |
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| spelling | Chiang, Hsiao-Dong Verfasser aut Stability regions of nonlinear dynamical systems theory, estimation, and applications Hsiao-Dong Chiang, Cornell University, Luís F.C. Alberto, University of Sao Paulo Cambridge Cambridge University Press 2015 1 Online-Ressource (X, 472 Seiten) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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; 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 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 Stability Dynamics Nonlinear control theory Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 s Ljapunov-Stabilitätstheorie (DE-588)4167992-1 s DE-604 Alberto, Luís F. C. Verfasser (DE-588)1079181261 aut Erscheint auch als Druckausgabe 978-1-107-03540-9 https://doi.org/10.1017/CBO9781139548861 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Chiang, Hsiao-Dong Alberto, Luís F. C. Stability regions of nonlinear dynamical systems theory, estimation, and applications 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; 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 Stability Dynamics Nonlinear control theory Nichtlineares dynamisches System (DE-588)4126142-2 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd |
| subject_GND | (DE-588)4126142-2 (DE-588)4167992-1 |
| title | Stability regions of nonlinear dynamical systems theory, estimation, and applications |
| title_auth | Stability regions of nonlinear dynamical systems theory, estimation, and applications |
| title_exact_search | Stability regions of nonlinear dynamical systems theory, estimation, and applications |
| title_full | Stability regions of nonlinear dynamical systems theory, estimation, and applications Hsiao-Dong Chiang, Cornell University, Luís F.C. Alberto, University of Sao Paulo |
| title_fullStr | Stability regions of nonlinear dynamical systems theory, estimation, and applications Hsiao-Dong Chiang, Cornell University, Luís F.C. Alberto, University of Sao Paulo |
| title_full_unstemmed | Stability regions of nonlinear dynamical systems theory, estimation, and applications Hsiao-Dong Chiang, Cornell University, Luís F.C. Alberto, University of Sao Paulo |
| title_short | Stability regions of nonlinear dynamical systems |
| title_sort | stability regions of nonlinear dynamical systems theory estimation and applications |
| title_sub | theory, estimation, and applications |
| topic | Stability Dynamics Nonlinear control theory Nichtlineares dynamisches System (DE-588)4126142-2 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd |
| topic_facet | Stability Dynamics Nonlinear control theory Nichtlineares dynamisches System Ljapunov-Stabilitätstheorie |
| url | https://doi.org/10.1017/CBO9781139548861 |
| work_keys_str_mv | AT chianghsiaodong stabilityregionsofnonlineardynamicalsystemstheoryestimationandapplications AT albertoluisfc stabilityregionsofnonlineardynamicalsystemstheoryestimationandapplications |