Save up to 30% on Elsevier print and eBooks with free shipping. No promo code needed.
Save up to 30% on print and eBooks.
Control and Estimation of Piecewise Affine Systems
1st Edition - March 28, 2014
Authors: Jun Xu, Lihua Xie
Language: English
Hardback ISBN:9781782421610
9 7 8 - 1 - 7 8 2 4 2 - 1 6 1 - 0
eBook ISBN:9781782421627
9 7 8 - 1 - 7 8 2 4 2 - 1 6 2 - 7
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 Piece…Read more
Purchase options
LIMITED OFFER
Save 50% on book bundles
Immediately download your ebook while waiting for your print delivery. No promo code is needed.
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.
Provides new insights on properties of PWA systems, including stability, stabilizability, reachability and controllability
Presents a unified framework for analysis and synthesis of both continuous-time and discrete-time PWA systems
Presents novel approaches for stability analysis and control design based on the promising SOS techniques
Academic researchers and engineers in systems theory and control technologies
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
No. of pages: 254
Language: English
Edition: 1
Published: March 28, 2014
Imprint: Woodhead Publishing
Hardback ISBN: 9781782421610
eBook ISBN: 9781782421627
JX
Jun Xu
Jun Xu is a staff engineer in the Department of Advance Servo Technology, Western Digital, Singapore.
Affiliations and expertise
Western Digital
LX
Lihua Xie
Lihua Xie is a professor in Department of Control and Instrumentation, Nanyang Technological University, Singapore. He is a Fellow of the IEEE and IFAC.
Affiliations and expertise
Nanyang Technological University, Singapore
Read Control and Estimation of Piecewise Affine Systems on ScienceDirect