Control and Estimation of Piecewise Affine Systems
Published on 30. October 2018
Book
Paperback/Softback
254 pages
978-0-08-101541-4 (ISBN)
Description
As a powerful tool to study nonlinear systems and hybrid systems, piecewise affine (PWA) systems have been widely applied to mechanical systems. Control and Estimation of Piecewise Affine Systems presents several research findings relating to the control and estimation of PWA systems in one unified view.
Chapters in this title discuss stability results of PWA systems, using piecewise quadratic Lyapunov functions and piecewise homogeneous polynomial Lyapunov functions. Explicit necessary and sufficient conditions for the controllability and reachability of a class of PWA systems are considered along with controller and estimator design methods for PWA systems using linear matrix inequality (LMI) and bilinear matrix inequality (BMI) techniques. A PWA approach to a class of Takagi-Sugeno fuzzy system is discussed in depth. The book uses a number of mechanical systems, such as disk servo systems to illustrate the advantages of the proposed methods.
Chapters in this title discuss stability results of PWA systems, using piecewise quadratic Lyapunov functions and piecewise homogeneous polynomial Lyapunov functions. Explicit necessary and sufficient conditions for the controllability and reachability of a class of PWA systems are considered along with controller and estimator design methods for PWA systems using linear matrix inequality (LMI) and bilinear matrix inequality (BMI) techniques. A PWA approach to a class of Takagi-Sugeno fuzzy system is discussed in depth. The book uses a number of mechanical systems, such as disk servo systems to illustrate the advantages of the proposed methods.
More details
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Elsevier Science & Technology
Target group
Professional and scholarly
Academic researchers and engineering practitioners with interest in systems theory and control technologies.
Dimensions
Height: 234 mm
Width: 156 mm
ISBN-13
978-0-08-101541-4 (9780081015414)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Jun Xu | Lihua Xie
Control and Estimation of Piecewise Affine Systems
Book
03/2014
Woodhead Publishing Ltd
€205.01
Article exhausted; check different version
Persons
Jun Xu is a staff engineer in the Department of Advance Servo Technology, Western Digital, Singapore. Lihua Xie is a professor in Department of Control and Instrumentation, Nanyang Technological University, Singapore. He is a Fellow of the IEEE and IFAC.
Content
Dedication
List of Figures
List of Tables
Preface
Symbols and Acronyms
Logic Operators
Algebraic Operators
Sets and Set Operators
Others
Acronyms
1. Introduction
Abstract:
1.1 Motivations
1.2 Research objective and contributions
1.3 Organization of the book
Bibliography
2. Piecewise affine systems
Abstract:
2.1 Introduction
2.2 System model
2.3 Structural analysis
2.4 Applications in mechanical systems
2.5 Notes
Bibliography
3. Stability conditions based on PQLFs
Abstract:
3.1 Introduction
3.2 Piecewise quadratic Lyapunov functions
3.3 Notes
Bibliography
4. Stability conditions based on SOS polynomials
Abstract:
4.1 Introduction
4.2 Useful lemmas
4.3 SOS based stability results
4.4 Notes
Bibliography
5. Stability conditions based on vertex representation
Abstract:
5.1 Introduction
5.2 Useful lemmas
5.3 Partition-dependent Lyapunov function
5.4 Vertex-dependent Lyapunov function
5.5 Notes
Bibliography
6. Controllability and reachability
Abstract:
6.1 Introduction
6.2 Controllability
6.3 Reachability
6.4 Notes
Bibliography
7. H? and generalized H2 controller design for PWA systems
Abstract:
7.1 Introduction
7.2 State feedback control
7.3 Notes
Bibliography
8. H? and generalized H2 estimator design for PWA systems
Abstract:
8.1 Introduction
8.2 Estimator structure and problem statement
8.3 H? estimation
8.4 Generalized H2 estimation
8.5 Notes
Bibliography
9. A PWA approach to Takagi-Sugeno fuzzy logic systems
Abstract:
9.1 Introduction
9.2 Takagi-Sugeno fuzzy model
9.3 Stability analysis
9.4 Controller design
9.5 Notes
Bibliography
10. Control and estimation of mechanical systems
Abstract:
10.1 Electric motor driven pendulum
10.2 Hard disk servo system
Bibliography
Semidefinite programming
Bibliography
Some proofs
B.1 Proof of Theorem 6.2.4
B.2 Proof of Theorem 6.2.5
B.3 Proof of Theorem 6.2.6
B.4 Proof of Theorem 6.3.2
Index
List of Figures
List of Tables
Preface
Symbols and Acronyms
Logic Operators
Algebraic Operators
Sets and Set Operators
Others
Acronyms
1. Introduction
Abstract:
1.1 Motivations
1.2 Research objective and contributions
1.3 Organization of the book
Bibliography
2. Piecewise affine systems
Abstract:
2.1 Introduction
2.2 System model
2.3 Structural analysis
2.4 Applications in mechanical systems
2.5 Notes
Bibliography
3. Stability conditions based on PQLFs
Abstract:
3.1 Introduction
3.2 Piecewise quadratic Lyapunov functions
3.3 Notes
Bibliography
4. Stability conditions based on SOS polynomials
Abstract:
4.1 Introduction
4.2 Useful lemmas
4.3 SOS based stability results
4.4 Notes
Bibliography
5. Stability conditions based on vertex representation
Abstract:
5.1 Introduction
5.2 Useful lemmas
5.3 Partition-dependent Lyapunov function
5.4 Vertex-dependent Lyapunov function
5.5 Notes
Bibliography
6. Controllability and reachability
Abstract:
6.1 Introduction
6.2 Controllability
6.3 Reachability
6.4 Notes
Bibliography
7. H? and generalized H2 controller design for PWA systems
Abstract:
7.1 Introduction
7.2 State feedback control
7.3 Notes
Bibliography
8. H? and generalized H2 estimator design for PWA systems
Abstract:
8.1 Introduction
8.2 Estimator structure and problem statement
8.3 H? estimation
8.4 Generalized H2 estimation
8.5 Notes
Bibliography
9. A PWA approach to Takagi-Sugeno fuzzy logic systems
Abstract:
9.1 Introduction
9.2 Takagi-Sugeno fuzzy model
9.3 Stability analysis
9.4 Controller design
9.5 Notes
Bibliography
10. Control and estimation of mechanical systems
Abstract:
10.1 Electric motor driven pendulum
10.2 Hard disk servo system
Bibliography
Semidefinite programming
Bibliography
Some proofs
B.1 Proof of Theorem 6.2.4
B.2 Proof of Theorem 6.2.5
B.3 Proof of Theorem 6.2.6
B.4 Proof of Theorem 6.3.2
Index