Piecewise Linear Control Systems: A Computational Approach
2. Piecewise Linear Modeling . . . . . . . . . . . . . . . . . . . . . 9 2. 1 Model Representation . . . . . . . . . . . . . . . . . . . . . 9 2. 2 Solution Concepts . . . . . . . . . . . . . . . . . . . . . . . 2. 3 Uncertainty Models . . . . . . . . . . . . . . . . . . . . . . 2. 4 Modularity and...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2003
|
| Schriftenreihe: | Lecture Notes in Control and Information Sciences
284 |
| Schlagworte: | |
| Online-Zugang: | FHI01 BTU01 Volltext |
| Zusammenfassung: | 2. Piecewise Linear Modeling . . . . . . . . . . . . . . . . . . . . . 9 2. 1 Model Representation . . . . . . . . . . . . . . . . . . . . . 9 2. 2 Solution Concepts . . . . . . . . . . . . . . . . . . . . . . . 2. 3 Uncertainty Models . . . . . . . . . . . . . . . . . . . . . . 2. 4 Modularity and Interconnections . . . . . . . . . . . . . . 26 2. 5 Piecewise Linear Function Representations . . . . . . . . . 28 2. 6 Comments and References . . . . . . . . . . . . . . . . . . 30 3. Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3. 1 Equilibrium Points and the Steady State Characteristic . . 32 3. 2 Constraint Verification and Invariance . . . . . . . . . . . 35 3. 3 Detecting Attractive Sliding Modes on Cell Boundaries 37 3. 4 Comments and References . . . . . . . . . . . . . . . . . . 39 4. Lyapunov Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4. 1 Exponential Stability . . . . . . . . . . . . . . . . . . . . . . 41 4. 2 Quadratic Stability . . . . . . . . . . . . . . . . . . . . . . . 42 4. 3 Conservatism of Quadratic Stability . . . . . . . . . . . . . 46 4. 4 From Quadratic to Piecewise Quadratic . . . . . . . . . . . 48 4. 5 Interlude: Describing Partition Properties . . . . . . . . . 51 4. 6 Piecewise Quadratic Lyapunov Functions . . . . . . . . . 55 4. 7 Analysis of Piecewise Linear Differential Inclusions . . . . 61 4. 8 Analysis of Systems with Attractive Sliding Modes . . . . 63 4. 9 Improving Computational Efficiency . . . . . . . . . . . . 66 4. 10 Piecewise Linear Lyapunov Functions . . . . . . . . . . . 72 4. 11 A Unifying View . . . . . . . . . . . . . . . . . . . . . . . . 77 4. 12 Comments and References . . . . . . . . . . . . . . . . . . 82 5. Dissipativity Analysis . . . . . . . . . . . . . . . . . . . . . . . . 85 5. 1 Dissipativity Analysis via Convex Optimization . . . . . . 86 21 14 Contents Contents 5. 2 Computation of £2 induced Gain . . . . . . . . . . . . . . 88 5. 3 Estimation of Transient Energy . . . . . . . . . . . . . . . . 89 5. 4 Dissipative Systems with Quadratic Supply Rates . . . . . 91 5. 5 Comments and References . . . . . . . . . . . . . . . . . . 95 Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6. 1 Quadratic Stabilization of Piecewise Linear" Systems . . . 97 6. 2 Controller Synthesis based on Piecewise Quadratics . . . 98 6. 3 Comments and References . . . . . . . . . . . . . . . . . . 105 7. Selected Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 7. 1 Estimation of Regions of Attraction . . . . . . . . . . . . |
| Beschreibung: | 1 Online-Ressource (X, 202 p) |
| ISBN: | 9783540368014 |
| DOI: | 10.1007/3-540-36801-9 |
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| 520 | |a 2. Piecewise Linear Modeling . . . . . . . . . . . . . . . . . . . . . 9 2. 1 Model Representation . . . . . . . . . . . . . . . . . . . . . 9 2. 2 Solution Concepts . . . . . . . . . . . . . . . . . . . . . . . 2. 3 Uncertainty Models . . . . . . . . . . . . . . . . . . . . . . 2. 4 Modularity and Interconnections . . . . . . . . . . . . . . 26 2. 5 Piecewise Linear Function Representations . . . . . . . . . 28 2. 6 Comments and References . . . . . . . . . . . . . . . . . . 30 3. Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3. 1 Equilibrium Points and the Steady State Characteristic . . 32 3. 2 Constraint Verification and Invariance . . . . . . . . . . . 35 3. 3 Detecting Attractive Sliding Modes on Cell Boundaries 37 3. 4 Comments and References . . . . . . . . . . . . . . . . . . 39 4. Lyapunov Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4. 1 Exponential Stability . . . . . . . . . . . . . . . . . . . . . . 41 4. | ||
| 520 | |a 2 Quadratic Stability . . . . . . . . . . . . . . . . . . . . . . . 42 4. 3 Conservatism of Quadratic Stability . . . . . . . . . . . . . 46 4. 4 From Quadratic to Piecewise Quadratic . . . . . . . . . . . 48 4. 5 Interlude: Describing Partition Properties . . . . . . . . . 51 4. 6 Piecewise Quadratic Lyapunov Functions . . . . . . . . . 55 4. 7 Analysis of Piecewise Linear Differential Inclusions . . . . 61 4. 8 Analysis of Systems with Attractive Sliding Modes . . . . 63 4. 9 Improving Computational Efficiency . . . . . . . . . . . . 66 4. 10 Piecewise Linear Lyapunov Functions . . . . . . . . . . . 72 4. 11 A Unifying View . . . . . . . . . . . . . . . . . . . . . . . . 77 4. 12 Comments and References . . . . . . . . . . . . . . . . . . 82 5. Dissipativity Analysis . . . . . . . . . . . . . . . . . . . . . . . . 85 5. 1 Dissipativity Analysis via Convex Optimization . . . . . . 86 21 14 Contents Contents 5. 2 Computation of £2 induced Gain . . . . . . . . . . . . . . 88 5. | ||
| 520 | |a 3 Estimation of Transient Energy . . . . . . . . . . . . . . . . 89 5. 4 Dissipative Systems with Quadratic Supply Rates . . . . . 91 5. 5 Comments and References . . . . . . . . . . . . . . . . . . 95 Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6. 1 Quadratic Stabilization of Piecewise Linear" Systems . . . 97 6. 2 Controller Synthesis based on Piecewise Quadratics . . . 98 6. 3 Comments and References . . . . . . . . . . . . . . . . . . 105 7. Selected Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 7. 1 Estimation of Regions of Attraction . . . . . . . . . . . . | ||
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Datensatz im Suchindex
| _version_ | 1804178820368957440 |
|---|---|
| any_adam_object | |
| author | Johansson, Mikael |
| author_facet | Johansson, Mikael |
| author_role | aut |
| author_sort | Johansson, Mikael |
| author_variant | m j mj |
| building | Verbundindex |
| bvnumber | BV045149149 |
| classification_rvk | SI 845 |
| collection | ZDB-2-ENG |
| ctrlnum | (ZDB-2-ENG)978-3-540-36801-4 (OCoLC)845566154 (DE-599)BVBBV045149149 |
| dewey-full | 629.8 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 629 - Other branches of engineering |
| dewey-raw | 629.8 |
| dewey-search | 629.8 |
| dewey-sort | 3629.8 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| doi_str_mv | 10.1007/3-540-36801-9 |
| format | Electronic eBook |
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| id | DE-604.BV045149149 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:10:03Z |
| institution | BVB |
| isbn | 9783540368014 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030538848 |
| oclc_num | 845566154 |
| open_access_boolean | |
| owner | DE-573 DE-634 |
| owner_facet | DE-573 DE-634 |
| physical | 1 Online-Ressource (X, 202 p) |
| psigel | ZDB-2-ENG ZDB-2-ENG_2000/2004 ZDB-2-ENG ZDB-2-ENG_2000/2004 ZDB-2-ENG ZDB-2-ENG_Archiv |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Lecture Notes in Control and Information Sciences |
| spelling | Johansson, Mikael Verfasser aut Piecewise Linear Control Systems A Computational Approach by Mikael Johansson Berlin, Heidelberg Springer Berlin Heidelberg 2003 1 Online-Ressource (X, 202 p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Control and Information Sciences 284 2. Piecewise Linear Modeling . . . . . . . . . . . . . . . . . . . . . 9 2. 1 Model Representation . . . . . . . . . . . . . . . . . . . . . 9 2. 2 Solution Concepts . . . . . . . . . . . . . . . . . . . . . . . 2. 3 Uncertainty Models . . . . . . . . . . . . . . . . . . . . . . 2. 4 Modularity and Interconnections . . . . . . . . . . . . . . 26 2. 5 Piecewise Linear Function Representations . . . . . . . . . 28 2. 6 Comments and References . . . . . . . . . . . . . . . . . . 30 3. Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3. 1 Equilibrium Points and the Steady State Characteristic . . 32 3. 2 Constraint Verification and Invariance . . . . . . . . . . . 35 3. 3 Detecting Attractive Sliding Modes on Cell Boundaries 37 3. 4 Comments and References . . . . . . . . . . . . . . . . . . 39 4. Lyapunov Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4. 1 Exponential Stability . . . . . . . . . . . . . . . . . . . . . . 41 4. 2 Quadratic Stability . . . . . . . . . . . . . . . . . . . . . . . 42 4. 3 Conservatism of Quadratic Stability . . . . . . . . . . . . . 46 4. 4 From Quadratic to Piecewise Quadratic . . . . . . . . . . . 48 4. 5 Interlude: Describing Partition Properties . . . . . . . . . 51 4. 6 Piecewise Quadratic Lyapunov Functions . . . . . . . . . 55 4. 7 Analysis of Piecewise Linear Differential Inclusions . . . . 61 4. 8 Analysis of Systems with Attractive Sliding Modes . . . . 63 4. 9 Improving Computational Efficiency . . . . . . . . . . . . 66 4. 10 Piecewise Linear Lyapunov Functions . . . . . . . . . . . 72 4. 11 A Unifying View . . . . . . . . . . . . . . . . . . . . . . . . 77 4. 12 Comments and References . . . . . . . . . . . . . . . . . . 82 5. Dissipativity Analysis . . . . . . . . . . . . . . . . . . . . . . . . 85 5. 1 Dissipativity Analysis via Convex Optimization . . . . . . 86 21 14 Contents Contents 5. 2 Computation of £2 induced Gain . . . . . . . . . . . . . . 88 5. 3 Estimation of Transient Energy . . . . . . . . . . . . . . . . 89 5. 4 Dissipative Systems with Quadratic Supply Rates . . . . . 91 5. 5 Comments and References . . . . . . . . . . . . . . . . . . 95 Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6. 1 Quadratic Stabilization of Piecewise Linear" Systems . . . 97 6. 2 Controller Synthesis based on Piecewise Quadratics . . . 98 6. 3 Comments and References . . . . . . . . . . . . . . . . . . 105 7. Selected Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 7. 1 Estimation of Regions of Attraction . . . . . . . . . . . . Engineering Control Theory of Computation Control, Robotics, Mechatronics Vibration, Dynamical Systems, Control Appl.Mathematics/Computational Methods of Engineering Systems Theory, Control Computers System theory Applied mathematics Engineering mathematics Vibration Dynamical systems Dynamics Control engineering Robotics Mechatronics Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd rswk-swf Fuzzy-Regelung (DE-588)4395755-9 gnd rswk-swf Reglerentwurf (DE-588)4177447-4 gnd rswk-swf Lineares Regelungssystem (DE-588)4167730-4 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Hybrides System (DE-588)4510314-8 gnd rswk-swf Lineares Regelungssystem (DE-588)4167730-4 s Reglerentwurf (DE-588)4177447-4 s Fuzzy-Regelung (DE-588)4395755-9 s Hybrides System (DE-588)4510314-8 s Dynamisches System (DE-588)4013396-5 s Ljapunov-Stabilitätstheorie (DE-588)4167992-1 s 1\p DE-604 Erscheint auch als Druck-Ausgabe 9783540441243 https://doi.org/10.1007/3-540-36801-9 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Johansson, Mikael Piecewise Linear Control Systems A Computational Approach Engineering Control Theory of Computation Control, Robotics, Mechatronics Vibration, Dynamical Systems, Control Appl.Mathematics/Computational Methods of Engineering Systems Theory, Control Computers System theory Applied mathematics Engineering mathematics Vibration Dynamical systems Dynamics Control engineering Robotics Mechatronics Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd Fuzzy-Regelung (DE-588)4395755-9 gnd Reglerentwurf (DE-588)4177447-4 gnd Lineares Regelungssystem (DE-588)4167730-4 gnd Dynamisches System (DE-588)4013396-5 gnd Hybrides System (DE-588)4510314-8 gnd |
| subject_GND | (DE-588)4167992-1 (DE-588)4395755-9 (DE-588)4177447-4 (DE-588)4167730-4 (DE-588)4013396-5 (DE-588)4510314-8 |
| title | Piecewise Linear Control Systems A Computational Approach |
| title_auth | Piecewise Linear Control Systems A Computational Approach |
| title_exact_search | Piecewise Linear Control Systems A Computational Approach |
| title_full | Piecewise Linear Control Systems A Computational Approach by Mikael Johansson |
| title_fullStr | Piecewise Linear Control Systems A Computational Approach by Mikael Johansson |
| title_full_unstemmed | Piecewise Linear Control Systems A Computational Approach by Mikael Johansson |
| title_short | Piecewise Linear Control Systems |
| title_sort | piecewise linear control systems a computational approach |
| title_sub | A Computational Approach |
| topic | Engineering Control Theory of Computation Control, Robotics, Mechatronics Vibration, Dynamical Systems, Control Appl.Mathematics/Computational Methods of Engineering Systems Theory, Control Computers System theory Applied mathematics Engineering mathematics Vibration Dynamical systems Dynamics Control engineering Robotics Mechatronics Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd Fuzzy-Regelung (DE-588)4395755-9 gnd Reglerentwurf (DE-588)4177447-4 gnd Lineares Regelungssystem (DE-588)4167730-4 gnd Dynamisches System (DE-588)4013396-5 gnd Hybrides System (DE-588)4510314-8 gnd |
| topic_facet | Engineering Control Theory of Computation Control, Robotics, Mechatronics Vibration, Dynamical Systems, Control Appl.Mathematics/Computational Methods of Engineering Systems Theory, Control Computers System theory Applied mathematics Engineering mathematics Vibration Dynamical systems Dynamics Control engineering Robotics Mechatronics Ljapunov-Stabilitätstheorie Fuzzy-Regelung Reglerentwurf Lineares Regelungssystem Dynamisches System Hybrides System |
| url | https://doi.org/10.1007/3-540-36801-9 |
| work_keys_str_mv | AT johanssonmikael piecewiselinearcontrolsystemsacomputationalapproach |