Stability of stationary sets in control systems with discontinuous nonlinearities /:
This book presents a development of the frequency-domain approach to the stability study of stationary sets of systems with discontinuous nonlinearities. The treatment is based on the theory of differential inclusions and the second Lyapunov method. Various versions of the Kalman-Yakubovich lemma on...
Gespeichert in:
| 1. Verfasser: | |
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| Weitere Verfasser: | , |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
River Edge, NJ :
World Scientific,
©2004.
|
| Schriftenreihe: | Series on stability, vibration, and control of systems.
v. 14. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book presents a development of the frequency-domain approach to the stability study of stationary sets of systems with discontinuous nonlinearities. The treatment is based on the theory of differential inclusions and the second Lyapunov method. Various versions of the Kalman-Yakubovich lemma on solvability of matrix inequalities are presented and discussed in detail. It is shown how the tools developed can be applied to stability investigations of relay control systems, gyroscopic systems, mechanical systems with a Coulomb friction, nonlinear electrical circuits, cellular neural networks, phase-locked loops, and synchronous machines. |
| Beschreibung: | 1 online resource (xv, 334 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 323-332) and index. |
| ISBN: | 9789812794239 9812794239 |
Internformat
MARC
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| 245 | 1 | 0 | |a Stability of stationary sets in control systems with discontinuous nonlinearities / |c V.A. Yakubovich, G.A. Leonov, A. Kh. Gelig. |
| 260 | |a River Edge, NJ : |b World Scientific, |c ©2004. | ||
| 300 | |a 1 online resource (xv, 334 pages) : |b illustrations | ||
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| 490 | 1 | |a Series on stability, vibration, and control of systems. Series A ; |v v. 14 | |
| 504 | |a Includes bibliographical references (pages 323-332) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 1. Foundations of theory of differential equations with discontinuous right-hand sides. 1.1. Notion of solution to differential equation with discontinuous right-hand side. 1.2. Systems of differential equations with multiple-valued right-hand sides (differential inclusions). 1.3. Dichotomy and stability -- 2. Auxiliary algebraic statements on solutions of matrix inequalities of a special type. 2.1. Algebraic problems that occur when finding conditions for the existence of Lyapunov functions from some multiparameter functional class. Circle criterion. Popov criterion. 2.2. Relevant algebraic statements -- 3. Dichotomy and stability of nonlinear systems with multiple equilibria. 3.1. Systems with piecewise single-valued nonlinearities. 3.2. Systems with monotone piecewise single-valued nonlinearities. 3.3. Systems with gradient nonlinearities -- 4. Stability of equilibria sets of pendulum-like systems. 4.1. Formulation of the stability problem for equilibrium sets of pendulum-like systems. 4.2. The method of periodic Lyapunov functions. 4.3. An analogue of the circle criterion for pendulum-like systems. 4.4. The method of non-local reduction. 4.5. Necessary conditions for gradient-like behavior of pendulum-like systems. 4.6. Stability of the dynamical systems describing the synchronous machines -- 5. Appendix. Proofs of the theorems of chapter 2. 5.1. Proofs of theorems on controllability, observability, irreducibility, and of lemmas 2.4 and 2.7. 5.2. Proof of theorem 2.13 (nonsingular Case). Theorem on solutions of Lur'e equation (algebraic Riccati equation). 5.3. Proof of theorem 2.13 (completion) and lemma 5.1. 5.4. Proofs of theorems 2.12 and 2.14 (singular Case). 5.5. Proofs of theorems 2.17-2.19 on losslessness of S-procedure. | |
| 520 | |a This book presents a development of the frequency-domain approach to the stability study of stationary sets of systems with discontinuous nonlinearities. The treatment is based on the theory of differential inclusions and the second Lyapunov method. Various versions of the Kalman-Yakubovich lemma on solvability of matrix inequalities are presented and discussed in detail. It is shown how the tools developed can be applied to stability investigations of relay control systems, gyroscopic systems, mechanical systems with a Coulomb friction, nonlinear electrical circuits, cellular neural networks, phase-locked loops, and synchronous machines. | ||
| 650 | 0 | |a Control theory. |0 http://id.loc.gov/authorities/subjects/sh85031658 | |
| 650 | 0 | |a Nonlinear control theory. |0 http://id.loc.gov/authorities/subjects/sh90000979 | |
| 650 | 0 | |a Set theory. |0 http://id.loc.gov/authorities/subjects/sh85120387 | |
| 650 | 0 | |a System analysis. | |
| 650 | 0 | |a Differential equations, Nonlinear. |0 http://id.loc.gov/authorities/subjects/sh85037906 | |
| 650 | 0 | |a Engineering mathematics. |0 http://id.loc.gov/authorities/subjects/sh85043235 | |
| 650 | 0 | |a Engineering systems. |0 http://id.loc.gov/authorities/subjects/sh2003006740 | |
| 650 | 2 | |a Systems Analysis |0 https://id.nlm.nih.gov/mesh/D013597 | |
| 650 | 6 | |a Théorie de la commande. | |
| 650 | 6 | |a Commande non linéaire. | |
| 650 | 6 | |a Théorie des ensembles. | |
| 650 | 6 | |a Analyse de systèmes. | |
| 650 | 6 | |a Équations différentielles non linéaires. | |
| 650 | 6 | |a Mathématiques de l'ingénieur. | |
| 650 | 6 | |a Systèmes d'ingénierie. | |
| 650 | 7 | |a systems analysis. |2 aat | |
| 650 | 7 | |a TECHNOLOGY & ENGINEERING |x Automation. |2 bisacsh | |
| 650 | 7 | |a TECHNOLOGY & ENGINEERING |x Robotics. |2 bisacsh | |
| 650 | 7 | |a Control theory |2 fast | |
| 650 | 7 | |a Differential equations, Nonlinear |2 fast | |
| 650 | 7 | |a Engineering mathematics |2 fast | |
| 650 | 7 | |a Engineering systems |2 fast | |
| 650 | 7 | |a Nonlinear control theory |2 fast | |
| 650 | 7 | |a Set theory |2 fast | |
| 650 | 7 | |a System analysis |2 fast | |
| 650 | 1 | 7 | |a Controleleer. |2 gtt |
| 650 | 1 | 7 | |a Verzamelingen (wiskunde) |2 gtt |
| 650 | 1 | 7 | |a Systeemtheorie. |2 gtt |
| 650 | 1 | 7 | |a Systeemanalyse. |2 gtt |
| 700 | 1 | |a Leonov, G. A. |q (Gennadiĭ Alekseevich) |1 https://id.oclc.org/worldcat/entity/E39PBJvmJypxykHRV3VFYxWMT3 |0 http://id.loc.gov/authorities/names/n80055061 | |
| 700 | 1 | |a Gelig, Arkadiĭ Khaĭmovich. | |
| 758 | |i has work: |a Stability of stationary sets in control systems with discontinuous nonlinearities (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGfQJ4VQpwKtW8T9tFmdjP |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a I︠A︡kubovich, V.A. (Vladimir Andreevich). |t Stability of stationary sets in control systems with discontinuous nonlinearities. |d River Edge, NJ : World Scientific, ©2004 |z 9812387196 |z 9789812387196 |w (DLC) 2005297772 |w (OCoLC)55875661 |
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| adam_text | |
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| author | I︠A︡kubovich, V. A. (Vladimir Andreevich) |
| author2 | Leonov, G. A. (Gennadiĭ Alekseevich) Gelig, Arkadiĭ Khaĭmovich |
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| author_GND | http://id.loc.gov/authorities/names/n82130491 http://id.loc.gov/authorities/names/n80055061 |
| author_facet | I︠A︡kubovich, V. A. (Vladimir Andreevich) Leonov, G. A. (Gennadiĭ Alekseevich) Gelig, Arkadiĭ Khaĭmovich |
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| callnumber-raw | QA402.3 .I248 2004eb |
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| contents | 1. Foundations of theory of differential equations with discontinuous right-hand sides. 1.1. Notion of solution to differential equation with discontinuous right-hand side. 1.2. Systems of differential equations with multiple-valued right-hand sides (differential inclusions). 1.3. Dichotomy and stability -- 2. Auxiliary algebraic statements on solutions of matrix inequalities of a special type. 2.1. Algebraic problems that occur when finding conditions for the existence of Lyapunov functions from some multiparameter functional class. Circle criterion. Popov criterion. 2.2. Relevant algebraic statements -- 3. Dichotomy and stability of nonlinear systems with multiple equilibria. 3.1. Systems with piecewise single-valued nonlinearities. 3.2. Systems with monotone piecewise single-valued nonlinearities. 3.3. Systems with gradient nonlinearities -- 4. Stability of equilibria sets of pendulum-like systems. 4.1. Formulation of the stability problem for equilibrium sets of pendulum-like systems. 4.2. The method of periodic Lyapunov functions. 4.3. An analogue of the circle criterion for pendulum-like systems. 4.4. The method of non-local reduction. 4.5. Necessary conditions for gradient-like behavior of pendulum-like systems. 4.6. Stability of the dynamical systems describing the synchronous machines -- 5. Appendix. Proofs of the theorems of chapter 2. 5.1. Proofs of theorems on controllability, observability, irreducibility, and of lemmas 2.4 and 2.7. 5.2. Proof of theorem 2.13 (nonsingular Case). Theorem on solutions of Lur'e equation (algebraic Riccati equation). 5.3. Proof of theorem 2.13 (completion) and lemma 5.1. 5.4. Proofs of theorems 2.12 and 2.14 (singular Case). 5.5. Proofs of theorems 2.17-2.19 on losslessness of S-procedure. |
| ctrlnum | (OCoLC)262616624 |
| dewey-full | 629.836 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 629 - Other branches of engineering |
| dewey-raw | 629.836 |
| dewey-search | 629.836 |
| dewey-sort | 3629.836 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| format | Electronic eBook |
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Dichotomy and stability of nonlinear systems with multiple equilibria. 3.1. Systems with piecewise single-valued nonlinearities. 3.2. Systems with monotone piecewise single-valued nonlinearities. 3.3. Systems with gradient nonlinearities -- 4. Stability of equilibria sets of pendulum-like systems. 4.1. Formulation of the stability problem for equilibrium sets of pendulum-like systems. 4.2. The method of periodic Lyapunov functions. 4.3. An analogue of the circle criterion for pendulum-like systems. 4.4. The method of non-local reduction. 4.5. Necessary conditions for gradient-like behavior of pendulum-like systems. 4.6. Stability of the dynamical systems describing the synchronous machines -- 5. Appendix. Proofs of the theorems of chapter 2. 5.1. Proofs of theorems on controllability, observability, irreducibility, and of lemmas 2.4 and 2.7. 5.2. Proof of theorem 2.13 (nonsingular Case). Theorem on solutions of Lur'e equation (algebraic Riccati equation). 5.3. 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| id | ZDB-4-EBA-ocn262616624 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:16:33Z |
| institution | BVB |
| isbn | 9789812794239 9812794239 |
| language | English |
| oclc_num | 262616624 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xv, 334 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | World Scientific, |
| record_format | marc |
| series | Series on stability, vibration, and control of systems. |
| series2 | Series on stability, vibration, and control of systems. Series A ; |
| spelling | I︠A︡kubovich, V. A. (Vladimir Andreevich) https://id.oclc.org/worldcat/entity/E39PBJyWWXmmqbDcdGFqmqYF8C http://id.loc.gov/authorities/names/n82130491 Stability of stationary sets in control systems with discontinuous nonlinearities / V.A. Yakubovich, G.A. Leonov, A. Kh. Gelig. River Edge, NJ : World Scientific, ©2004. 1 online resource (xv, 334 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Series on stability, vibration, and control of systems. Series A ; v. 14 Includes bibliographical references (pages 323-332) and index. Print version record. 1. Foundations of theory of differential equations with discontinuous right-hand sides. 1.1. Notion of solution to differential equation with discontinuous right-hand side. 1.2. Systems of differential equations with multiple-valued right-hand sides (differential inclusions). 1.3. Dichotomy and stability -- 2. Auxiliary algebraic statements on solutions of matrix inequalities of a special type. 2.1. Algebraic problems that occur when finding conditions for the existence of Lyapunov functions from some multiparameter functional class. Circle criterion. Popov criterion. 2.2. Relevant algebraic statements -- 3. Dichotomy and stability of nonlinear systems with multiple equilibria. 3.1. Systems with piecewise single-valued nonlinearities. 3.2. Systems with monotone piecewise single-valued nonlinearities. 3.3. Systems with gradient nonlinearities -- 4. Stability of equilibria sets of pendulum-like systems. 4.1. Formulation of the stability problem for equilibrium sets of pendulum-like systems. 4.2. The method of periodic Lyapunov functions. 4.3. An analogue of the circle criterion for pendulum-like systems. 4.4. The method of non-local reduction. 4.5. Necessary conditions for gradient-like behavior of pendulum-like systems. 4.6. Stability of the dynamical systems describing the synchronous machines -- 5. Appendix. Proofs of the theorems of chapter 2. 5.1. Proofs of theorems on controllability, observability, irreducibility, and of lemmas 2.4 and 2.7. 5.2. Proof of theorem 2.13 (nonsingular Case). Theorem on solutions of Lur'e equation (algebraic Riccati equation). 5.3. Proof of theorem 2.13 (completion) and lemma 5.1. 5.4. Proofs of theorems 2.12 and 2.14 (singular Case). 5.5. Proofs of theorems 2.17-2.19 on losslessness of S-procedure. This book presents a development of the frequency-domain approach to the stability study of stationary sets of systems with discontinuous nonlinearities. The treatment is based on the theory of differential inclusions and the second Lyapunov method. Various versions of the Kalman-Yakubovich lemma on solvability of matrix inequalities are presented and discussed in detail. It is shown how the tools developed can be applied to stability investigations of relay control systems, gyroscopic systems, mechanical systems with a Coulomb friction, nonlinear electrical circuits, cellular neural networks, phase-locked loops, and synchronous machines. Control theory. http://id.loc.gov/authorities/subjects/sh85031658 Nonlinear control theory. http://id.loc.gov/authorities/subjects/sh90000979 Set theory. http://id.loc.gov/authorities/subjects/sh85120387 System analysis. Differential equations, Nonlinear. http://id.loc.gov/authorities/subjects/sh85037906 Engineering mathematics. http://id.loc.gov/authorities/subjects/sh85043235 Engineering systems. http://id.loc.gov/authorities/subjects/sh2003006740 Systems Analysis https://id.nlm.nih.gov/mesh/D013597 Théorie de la commande. Commande non linéaire. Théorie des ensembles. Analyse de systèmes. Équations différentielles non linéaires. Mathématiques de l'ingénieur. Systèmes d'ingénierie. systems analysis. aat TECHNOLOGY & ENGINEERING Automation. bisacsh TECHNOLOGY & ENGINEERING Robotics. bisacsh Control theory fast Differential equations, Nonlinear fast Engineering mathematics fast Engineering systems fast Nonlinear control theory fast Set theory fast System analysis fast Controleleer. gtt Verzamelingen (wiskunde) gtt Systeemtheorie. gtt Systeemanalyse. gtt Leonov, G. A. (Gennadiĭ Alekseevich) https://id.oclc.org/worldcat/entity/E39PBJvmJypxykHRV3VFYxWMT3 http://id.loc.gov/authorities/names/n80055061 Gelig, Arkadiĭ Khaĭmovich. has work: Stability of stationary sets in control systems with discontinuous nonlinearities (Text) https://id.oclc.org/worldcat/entity/E39PCGfQJ4VQpwKtW8T9tFmdjP https://id.oclc.org/worldcat/ontology/hasWork Print version: I︠A︡kubovich, V.A. (Vladimir Andreevich). Stability of stationary sets in control systems with discontinuous nonlinearities. River Edge, NJ : World Scientific, ©2004 9812387196 9789812387196 (DLC) 2005297772 (OCoLC)55875661 Series on stability, vibration, and control of systems. Series A ; v. 14. http://id.loc.gov/authorities/names/n97060398 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235597 Volltext |
| spellingShingle | I︠A︡kubovich, V. A. (Vladimir Andreevich) Stability of stationary sets in control systems with discontinuous nonlinearities / Series on stability, vibration, and control of systems. 1. Foundations of theory of differential equations with discontinuous right-hand sides. 1.1. Notion of solution to differential equation with discontinuous right-hand side. 1.2. Systems of differential equations with multiple-valued right-hand sides (differential inclusions). 1.3. Dichotomy and stability -- 2. Auxiliary algebraic statements on solutions of matrix inequalities of a special type. 2.1. Algebraic problems that occur when finding conditions for the existence of Lyapunov functions from some multiparameter functional class. Circle criterion. Popov criterion. 2.2. Relevant algebraic statements -- 3. Dichotomy and stability of nonlinear systems with multiple equilibria. 3.1. Systems with piecewise single-valued nonlinearities. 3.2. Systems with monotone piecewise single-valued nonlinearities. 3.3. Systems with gradient nonlinearities -- 4. Stability of equilibria sets of pendulum-like systems. 4.1. Formulation of the stability problem for equilibrium sets of pendulum-like systems. 4.2. The method of periodic Lyapunov functions. 4.3. An analogue of the circle criterion for pendulum-like systems. 4.4. The method of non-local reduction. 4.5. Necessary conditions for gradient-like behavior of pendulum-like systems. 4.6. Stability of the dynamical systems describing the synchronous machines -- 5. Appendix. Proofs of the theorems of chapter 2. 5.1. Proofs of theorems on controllability, observability, irreducibility, and of lemmas 2.4 and 2.7. 5.2. Proof of theorem 2.13 (nonsingular Case). Theorem on solutions of Lur'e equation (algebraic Riccati equation). 5.3. Proof of theorem 2.13 (completion) and lemma 5.1. 5.4. Proofs of theorems 2.12 and 2.14 (singular Case). 5.5. Proofs of theorems 2.17-2.19 on losslessness of S-procedure. Control theory. http://id.loc.gov/authorities/subjects/sh85031658 Nonlinear control theory. http://id.loc.gov/authorities/subjects/sh90000979 Set theory. http://id.loc.gov/authorities/subjects/sh85120387 System analysis. Differential equations, Nonlinear. http://id.loc.gov/authorities/subjects/sh85037906 Engineering mathematics. http://id.loc.gov/authorities/subjects/sh85043235 Engineering systems. http://id.loc.gov/authorities/subjects/sh2003006740 Systems Analysis https://id.nlm.nih.gov/mesh/D013597 Théorie de la commande. Commande non linéaire. Théorie des ensembles. Analyse de systèmes. Équations différentielles non linéaires. Mathématiques de l'ingénieur. Systèmes d'ingénierie. systems analysis. aat TECHNOLOGY & ENGINEERING Automation. bisacsh TECHNOLOGY & ENGINEERING Robotics. bisacsh Control theory fast Differential equations, Nonlinear fast Engineering mathematics fast Engineering systems fast Nonlinear control theory fast Set theory fast System analysis fast Controleleer. gtt Verzamelingen (wiskunde) gtt Systeemtheorie. gtt Systeemanalyse. gtt |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85031658 http://id.loc.gov/authorities/subjects/sh90000979 http://id.loc.gov/authorities/subjects/sh85120387 http://id.loc.gov/authorities/subjects/sh85037906 http://id.loc.gov/authorities/subjects/sh85043235 http://id.loc.gov/authorities/subjects/sh2003006740 https://id.nlm.nih.gov/mesh/D013597 |
| title | Stability of stationary sets in control systems with discontinuous nonlinearities / |
| title_auth | Stability of stationary sets in control systems with discontinuous nonlinearities / |
| title_exact_search | Stability of stationary sets in control systems with discontinuous nonlinearities / |
| title_full | Stability of stationary sets in control systems with discontinuous nonlinearities / V.A. Yakubovich, G.A. Leonov, A. Kh. Gelig. |
| title_fullStr | Stability of stationary sets in control systems with discontinuous nonlinearities / V.A. Yakubovich, G.A. Leonov, A. Kh. Gelig. |
| title_full_unstemmed | Stability of stationary sets in control systems with discontinuous nonlinearities / V.A. Yakubovich, G.A. Leonov, A. Kh. Gelig. |
| title_short | Stability of stationary sets in control systems with discontinuous nonlinearities / |
| title_sort | stability of stationary sets in control systems with discontinuous nonlinearities |
| topic | Control theory. http://id.loc.gov/authorities/subjects/sh85031658 Nonlinear control theory. http://id.loc.gov/authorities/subjects/sh90000979 Set theory. http://id.loc.gov/authorities/subjects/sh85120387 System analysis. Differential equations, Nonlinear. http://id.loc.gov/authorities/subjects/sh85037906 Engineering mathematics. http://id.loc.gov/authorities/subjects/sh85043235 Engineering systems. http://id.loc.gov/authorities/subjects/sh2003006740 Systems Analysis https://id.nlm.nih.gov/mesh/D013597 Théorie de la commande. Commande non linéaire. Théorie des ensembles. Analyse de systèmes. Équations différentielles non linéaires. Mathématiques de l'ingénieur. Systèmes d'ingénierie. systems analysis. aat TECHNOLOGY & ENGINEERING Automation. bisacsh TECHNOLOGY & ENGINEERING Robotics. bisacsh Control theory fast Differential equations, Nonlinear fast Engineering mathematics fast Engineering systems fast Nonlinear control theory fast Set theory fast System analysis fast Controleleer. gtt Verzamelingen (wiskunde) gtt Systeemtheorie. gtt Systeemanalyse. gtt |
| topic_facet | Control theory. Nonlinear control theory. Set theory. System analysis. Differential equations, Nonlinear. Engineering mathematics. Engineering systems. Systems Analysis Théorie de la commande. Commande non linéaire. Théorie des ensembles. Analyse de systèmes. Équations différentielles non linéaires. Mathématiques de l'ingénieur. Systèmes d'ingénierie. systems analysis. TECHNOLOGY & ENGINEERING Automation. TECHNOLOGY & ENGINEERING Robotics. Control theory Differential equations, Nonlinear Engineering mathematics Engineering systems Nonlinear control theory Set theory System analysis Controleleer. Verzamelingen (wiskunde) Systeemtheorie. Systeemanalyse. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235597 |
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