Piecewise Linear Control Systems

A Computational Approach
2003
ISBN: 978-3-540-44124-3
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 284, 202 Seiten, Paperback, Format (B × H): 155 mm x 233 mm, Gewicht: 338 g

Reihe: Lecture Notes in Control and Information Sciences

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.

Zielgruppe

Research

Autoren/Hrsg.

Johansson, Mikael K. -J.

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Statik, Dynamik, Kinetik, Kinematik
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
• Technische Wissenschaften Technik Allgemein Mess- und Automatisierungstechnik
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Technische Wissenschaften Elektronik | Nachrichtentechnik Elektronik Überwachungstechnik

Inhaltsverzeichnis

Piecewise Linear Modeling.- Structural Analysis.- Lyapunov Stability.- Dissipativity Analysis.- Controller Design.- Selected Topics.- Linear Hybrid Dynamical Systems.- Concluding Remarks.