Control and Estimation of Piecewise Affine Systems

Author： Xu   Jun;Xie   Lihua  

Publisher： Elsevier Science‎

Publication year： 2014

E-ISBN: 9781782421627

P-ISBN(Paperback): 9781782421610

P-ISBN(Hardback):  9781782421610

Subject：

Language： ENG

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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.

  • 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

Chapter

Cover

Control and estimation of piecewise affine systems

Copyright

Dedication

Contents

List of Figures

List of Tables

Preface

Symbols and Acronyms

1 Introduction

1.1 Motivations

1.2 Research objective and contributions

1.3 Organization of the book

Bibliography

2 Piecewise affine systems

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

3.1 Introduction

3.2 Piecewise quadratic Lyapunov functions

3.3 Notes

Bibliography

4 Stability conditions based on SOS polynomials

4.1 Introduction

4.2 Useful lemmas

4.3 SOS based stability results

4.4 Notes

Bibliography

5 Stability conditions based on vertex representation

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

6.1 Introduction

6.2 Controllability

6.3 Reachability

6.4 Notes

Bibliography

7 H∞ and generalized H2 controller design for PWA systems

7.1 Introduction

7.2 State feedback control

7.3 Notes

Bibliography

8 H∞ and generalized H2 estimator design for PWA systems

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

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

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

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