Robust and H∞ Control

Ben M. Chen, National University of Singapore

Springer, New York, London, 2000 (¥ click on this link to order ¥)

Communications and Control Engineering Series, xii/446 pages / ISBN 1-85233-255-7    ... Errata List ...

From the Back Cover:

H∞ control theory deals with the minimization of the H∞ norm of the transfer matrix from an exogenous disturbance to a pertinent controlled output of a given plant. Robust and H∞ Control examines both the theoretical and practical aspects of H∞ control from the viewpoint of the structural properties of linear systems. Constructive algorithms are provided for finding solutions to:

Theories are also applied to real-life problems with actual implementations. This book can be used for graduate courses in departments of aeronautics and astronautics, applied mathematics, chemical engineering, electrical engineering and mechanical engineering. It should also be of great value to engineers practising in industry.

The Communications and Control Engineering series reflects the major technological advances that have a great impact in the fields of communication and control. It reports on research in industrial and academic institutions around the world to exploit the new possibilities that are becoming available.

Table of Contents 

 
 
   1 Introduction  {1}
     1.1 Introduction
     1.2 Notations
     1.3 The Standard H∞ Optimization Problem
     1.4 Some Common Robust Control Problems
         1.4.1 The Mixed-sensitivity Problem
         1.4.2 Maximization of Complex Stability Radius
         1.4.3 Robust Stabilization with Additive Perturbations
         1.4.4 Robust Stabilization with Multiplicative Perturbations
     1.5 Preview of Each Chapter
 
   2 Linear System Tools  {19}
     2.1 Introduction
     2.2 Jordan and Real Jordan Canonical Forms  
     2.3 Structural Decompositions of Matrix Pairs 
     2.4 Special Coordinate Basis  
     2.5 Proofs of Properties of Special Coordinate Basis  
 
   3 Structural Mappings of Bilinear Transformations  {57}
     3.1 Introduction  
     3.2 Mapping of Continuous-time to Discrete-time 
     3.3 Mapping of Discrete-time to Continuous-time 
     3.4 Proof of Theorem 3.2.1
 
   4 Existence Conditions of H∞ Suboptimal Controllers  {83}
     4.1 Introduction 
     4.2 Continuous-time Systems 
     4.3 Discrete-time Systems
 
   5 Solutions to Discrete-time Riccati Equations  {95}
     5.1 Introduction 
     5.2 Solution to a General DARE
     5.3 Solution to an H∞ DARE  
     5.4 Proofs of Main Results 
 
   6 Infima in Continuous-time H∞ Optimization  {111}
     6.1 Introduction  
     6.2 Full Information Feedback Case  
     6.3 Output Feedback Case 
     6.4 Plants with Imaginary Axis Zeros  
 
   7 Solutions to Continuous-time H∞ Problem  {143}
     7.1 Introduction
     7.2 Full State Feedback 
     7.3 Full Order Output Feedback
     7.4 Reduced Order Output Feedback 
     7.5 Proofs of Main Results 
 
   8 Continuous-time H∞ Almost Disturbance Decoupling  {177}
     8.1 Introduction  
     8.2 Solvability Conditions  
     8.3 Solutions to Full State Feedback Case  
     8.4 Solutions to Output Feedback Case 
         8.4.1 Full Order Output Feedback
         8.4.2 Reduced Order Output Feedback 
     8.5 Proofs of Main Results 
 
   9 Robust and Perfect Tracking of Continuous-time Systems  {215}
     9.1 Introduction 
     9.2 Solvability Conditions and Solutions 
         9.2.1 Solutions to State Feedback Case 
         9.2.2 Solutions to Measurement Feedback Case 
               A. Full Order Measurement Feedback 
               B. Reduced Order Measurement Feedback  
     9.3 Robust and Perfect Tracking for Other References 
     9.4 Proofs of Main Results  
 
  10 Infima in Discrete-time H∞ Optimization  {249}
     10.1 Introduction 
     10.2 Full Information Feedback Case  
     10.3 Output Feedback Case  
     10.4 Plants with Unit Circle Zeros 
 
  11 Solutions to Discrete-time H∞ Problem  {269}
     11.1 Introduction 
     11.2 Full Information and State Feedbacks  
     11.3 Full Order Output Feedback 
     11.4 Reduced Order Output Feedback 
 
  12 Discrete-time H∞ Almost Disturbance Decoupling  {287}
     12.1 Introduction 
     12.2 Solvability Conditions 
     12.3 Solutions to State and Full Information Feedback Cases 
     12.4 Solutions to Measurement Feedback Case 
          12.4.1 Full Order Output Feedback 
          12.4.2 Reduced Order Output Feedback 
     12.5 Proofs of Main Results 
 
  13 Robust and Perfect Tracking of Discrete-time Systems  {339}
     13.1 Introduction
     13.2 Solvability Conditions and Solutions  
          13.2.1 Solutions to State Feedback Case 
          13.2.2 Solutions to Measurement Feedback Case 
     13.3 An Almost Perfect Tracking Problem 
 
  14 Design of a Hard Disk Drive Servo System  {363}
     14.1 Introduction 
     14.2 Modeling of the VCM Actuator 
     14.3 Servo System Design and Simulation Results 
     14.4 Implementation Results 
 
  15 Design of a Piezoelectric Actuator System  {381}
     15.1 Introduction 
     15.2 Linearization of the Nonlinear Hysteretic Dynamics 
     15.3 Formulation of the Problem as an H∞ ADDPMS 
     15.4 Final Controller and Simulation Results 
 
  16 Design of a Gyro-stabilized Mirror Targeting System  {407}
     16.1 Introduction 
     16.2 The Free Gyro-stabilized Mirror System  
     16.3 Controller Design Using the RPT Approach  
     16.4 Simulation and Implementation Results  
 
     Bibliography  {429}
 
     Index  {443}
 

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