Discrete H-Infinity Optimazation

       Charles K. Chui   and   Guanrong Chen
          (Texas A&M)          (Univ. of Houston)

Springer Series in Information Sciences, Vol.26, Springer-Verlag,

First edition: Signal Processing and Systems Theory: Selected Topics, 1992

Second edition: Discrete H-infinity Optimization, 1997

%%%%%%%%%%%%%%%%%%%%%%%% OUTLINE of CONTENTS %%%%%%%%%%%%%%%%%%%%%%%%%%

1.  DIGITAL SIGNALS AND DIGITAL FILTERS ----------------------------- 1
1.1 Analog and Digital Signals -------------------------------------- 1
1.2 Time and Frequency Domains -------------------------------------- 8
1.3 z-Transforms --------------------------------------------------- 15 
1.4 Digital Filters ------------------------------------------------ 23 
1.5 Optimal Digital Filter Design Criteria ------------------------- 33 
       EXERCISES --------------------------------------------------- 41

2.  LINEAR SYSTEMS ------------------------------------------------- 51
2.1 State-Space Descriptions --------------------------------------- 51
2.2 Transfer Matrices and Minimal Realization ---------------------- 59
2.3 SISO Linear Systems -------------------------------------------- 67
2.4 Sensitivity and Feedback Systems ------------------------------- 77
       EXERCISES --------------------------------------------------- 95

3. APPROXIMATION IN HARDY SPACES ----------------------------------- 92
3.1 Hardy Spaces Preliminaries ------------------------------------- 93
3.2 Least-Squares Approximation ------------------------------------ 98
3.3 Minimum-Norm Interpolation ------------------------------------ 109
3.4 Nevanlinna-Pick Interpolation --------------------------------- 115
       EXERCISES -------------------------------------------------- 124

4.  OPTIMAL HANKEL-NORM APPROXIMATION AND H-infinity-MINIMIZATION - 129
4.1 The Nehari Theorem and Related Results ------------------------ 130
4.2 s-Numbers and Schmidt Pairs ----------------------------------- 139
4.3 Systems Reduction --------------------------------------------- 150
4.4 H-infinity-Minimization --------------------------------------- 163
       EXERCISES -------------------------------------------------- 176

5.  GENERAL THEORY OF OPTIMAL HANKEL-NORM APPROXIMATION ----------- 184 
5.1 Existence and Preliminary Results ----------------------------- 184
5.2 Uniqueness of Schmidt Pairs ----------------------------------- 203
5.3 The Greatest Common Divisor: the Inner Function f(z) ---------- 207  
5.4 AAK's Main Theorem on Best Hankel-Norm Approximation ---------- 215
       EXERCISES -------------------------------------------------- 221

6.  H-infinity-OPTIMIZATION AND SYSTEMS REDUCTION FOR MIMO SYSTEMS  227 
6.1 Balanced Realization of MIMO Linear Systems ------------------- 227 
6.2 Matrix-Valued All-pass Transfer Functions --------------------- 233
6.3 Optimal Hankel-Norm Approximation for MIMO Systems ------------ 241
       EXERCISES -------------------------------------------------- 264

BIBLIOGRAPHY ------------------------------------------------------ 270
LIST OF SYMBOLS --------------------------------------------------- 287
INDEX ------------------------------------------------------------- 288