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Linear Systems

Book Description

Linear Systems: Non-Fragile Control and Filtering presents the latest research results and a systematic approach to designing non-fragile controllers and filters for linear systems. The authors combine the algebraic Riccati technique, the linear matrix inequality (LMI) technique, and the sensitivity analysis method to establish a set of new non-fragile (insensitive) control methods. This proposed method can optimize the closed-loop system performance and make the designed controllers or filters tolerant of coefficient variations in controller or filter gain matrices.

A Systematic Approach to Designing Non-Fragile Controllers and Filters for Linear Systems

The text begins with developments and main research methods in non-fragile control. It then systematically presents novel methods for non-fragile control and filtering of linear systems with respect to additive/multiplicative controller/filter gain uncertainties. The book introduces the algebraic Riccati equation technique to solve additive/multiplicative norm-bounded controller/filter gain uncertainty, and proposes a structured vertex separator to deal with the numerical problem resulting from interval-bounded coefficient variations. It also explains how to design insensitive controllers and filters in the framework of coefficient sensitivity theory. Throughout, the book includes numerical examples to demonstrate the effectiveness of the proposed design methods.

More Effective Design Methods for Non-Fragile Controllers and Filters

The design and analysis tools described will help readers to better understand and analyze parameter uncertainties and to design more effective non-fragile controllers and filters. Providing a coherent approach, this book is a valuable reference for researchers, graduate students, and anyone who wants to explore the area of non-fragile control and filtering.

Table of Contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright Page
  5. Table of Contents
  6. Preface
  7. Symbol Description
  8. 1 Introduction
  9. 2 Preliminaries
    1. 2.1 Delta Operator Definition
    2. 2.2 H∞ Performance Index
    3. 2.3 Operations on Systems
    4. 2.4 Some Other Definitions and Lemmas
  10. 3 Non-Fragile State Feedback Control with Norm-Bounded Gain Uncertainty
    1. 3.1 Introduction
    2. 3.2 Problem Statement
    3. 3.3 Non-Fragile Guaranteed Cost Controller Design
      1. 3.3.1 Additive Controller Gain Uncertainty Case
      2. 3.3.2 Multiplicative Controller Gain Uncertainty Case
    4. 3.4 Example
    5. 3.5 Conclusion
  11. 4 Non-Fragile Dynamic Output Feedback Control with Norm-Bounded Gain Uncertainty
    1. 4.1 Introduction
    2. 4.2 Problem Statement
    3. 4.3 Non-Fragile H∞ Dynamic Output Feedback Controller Design
      1. 4.3.1 Additive Controller Gain Uncertainty Case
      2. 4.3.2 Multiplicative Controller Gain Uncertainty Case
    4. 4.4 Example
    5. 4.5 Conclusion
  12. 5 Robust Non-Fragile Kalman Filtering with Norm-Bounded Gain Uncertainty
    1. 5.1 Introduction
    2. 5.2 Problem Statement
    3. 5.3 Robust Non-Fragile Filter Design
      1. 5.3.1 Additive Gain Uncertainty Case
      2. 5.3.2 Multiplicative Gain Uncertainty Case
    4. 5.4 Example
    5. 5.5 Conclusion
  13. 6 Non-Fragile Output Feedback Control with Interval-Bounded Coefficient Variations
    1. 6.1 Introduction
    2. 6.2 Non-Fragile H∞ Controller Design for Discrete-Time Systems
      1. 6.2.1 Problem Statement
      2. 6.2.2 Non-Fragile H∞ Controller Design Methods
      3. 6.2.3 Example
    3. 6.3 Non-Fragile H∞ Controller Design for Continuous-Time Systems
      1. 6.3.1 Problem Statement
      2. 6.3.2 Non-Fragile H∞ Controller Design Methods
      3. 6.3.3 Example
    4. 6.4 Non-Fragile H∞ Controller Designs with Sparse Structures
      1. 6.4.1 Problem Statement
      2. 6.4.2 Sparse Structured Controller Design
      3. 6.4.3 Example
    5. 6.5 Conclusion
  14. 7 Non-Fragile H∞ Filtering with Interval-Bounded Coefficient Variations
    1. 7.1 Introduction
    2. 7.2 Non-Fragile H∞ Filtering for Discrete-Time Systems
      1. 7.2.1 Problem Statement
      2. 7.2.2 Non-Fragile H∞ Filter Design Methods
      3. 7.2.3 Example
    3. 7.3 Non-Fragile H∞ Filter Design for Linear Continuous-Time Systems
      1. 7.3.1 Problem Statement
      2. 7.3.2 Non-Fragile H∞ Filter Design Methods
      3. 7.3.3 Example
    4. 7.4 Sparse Structured H∞ Filter Design
      1. 7.4.1 Problem Statement
      2. 7.4.2 Non-Fragile H∞ Filter Design with Sparse Structures
      3. 7.4.3 Example
    5. 7.5 Conclusion
  15. 8 Insensitive H∞ Filtering of Continuous-Time Systems
    1. 8.1 Introduction
    2. 8.2 Problem Statement
    3. 8.3 Insensitive H∞ Filter Design
      1. 8.3.1 Additive Filter Coefficient Variation Case
      2. 8.3.2 Multiplicative Filter Coefficient Variation Case
    4. 8.4 Computation of Robust H∞ Performance Index
    5. 8.5 Comparison with the Existing Design Method
    6. 8.6 Example
    7. 8.7 Conclusion
  16. 9 Insensitive H∞ Filtering of Delta Operator Systems
    1. 9.1 Introduction
    2. 9.2 Problem Statement
    3. 9.3 Insensitive H∞ Filter Design
      1. 9.3.1 Additive Coefficient Variation Case
      2. 9.3.2 Multiplicative Filter Coefficient Variation Case
    4. 9.4 Example
    5. 9.5 Conclusion
  17. 10 Insensitive H∞ Output Tracking Control
    1. 10.1 Introduction
    2. 10.2 Problem Statement
    3. 10.3 Insensitive H∞ Tracking Control Design
    4. 10.4 Example
    5. 10.5 Conclusion
  18. 11 Insensitive H∞ Dynamic Output Feedback Control
    1. 11.1 Introduction
    2. 11.2 Problem Statement
      1. 11.2.1 Sensitivity Function
      2. 11.2.2 Sensitivity Measures
      3. 11.2.3 Insensitive H∞ Control with Controller Coefficient Variations
    3. 11.3 Insensitive H∞ Controller Design
      1. 11.3.1 Step 1: General Conditions for the Existence of Insensitive H∞ Controllers
      2. 11.3.2 Step 2: Non-Fragile H∞ Controller Design with Interval-Bounded Controller Coefficient Variations
      3. 11.3.3 Summary of the Approach
      4. 11.3.4 Insensitive H∞ Control with Multiplicative Controller Coefficient Variations
    4. 11.4 Example
    5. 11.5 Conclusion
  19. Bibliography
  20. Index