Control and Estimation of Piecewise Affine Systems

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.

• 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

• 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