• 1 Linear Systems: Some Prerequisites.- 1.1 State Space Description and Input/Output Map.- 1.2 Dichotomy. RL?, RH+? and RH?? Spaces.- 1.3 Hankel and Toeplitz Operators.- 1.4 Balanced Forms.- Notes and References.- 2 The Kalman-Popov-Yakubovich System of Indefinite Sign.- 2.1 Popov Triplets: Associated Objects, Equivalence, Duality.- 2.2 Basic Operators.- 2.3 The Stabilizing Solution.- 2.4 A Matrix Pencil Description.- 2.5 The Signature Condition.- Notes and References.- 3 H? Control: A Signature Condition Based Approach.- 3.1 Problem Statement.- 3.2 The Redheffer Theorem.- 3.3 A First Set of Necessary Solvability Conditions.- 3.4 A Second Set of Necessary Solvability Conditions.- 3.5 Coupled and Uncoupled Necessity Solvability Conditions.- 3.6 Sufficient Solvability Conditions: An Explicit Solution in KPYS Terms.- 3.7 Singular Problems: Necessary and Sufficient Conditions.- Notes and References.- 4 The Nehari Problem.- 4.1 The Two-Block Case.- 4.2 The One-Block Case.- Notes and References.- 5 Optimal H? Problems: A Singular Perturbation Approach.- 5.1 Optimal Solution of the H?- Control Problem.- 5.2 Case Studies.- Notes and References.- 6 Singular H? Problems.- 6.1 Robustness with Respect to Multiplicative Uncertainty.- 6.2 Sensitivity Minimization.- Notes and References.

'This is a useful book oriented to researchers, control systems engineers and applied mathematicians as well as to graduate students. Specialists in numerical computations will also find interesting issues in this book.' Mathematical Reviews

• 1 Linear Systems: Some Prerequisites.- 1.1 State Space Description and Input/Output Map.- 1.2 Dichotomy. RL?, RH+? and RH?? Spaces.- 1.3 Hankel and Toeplitz Operators.- 1.4 Balanced Forms.- Notes and References.- 2 The Kalman-Popov-Yakubovich System of Indefinite Sign.- 2.1 Popov Triplets: Associated Objects, Equivalence, Duality.- 2.2 Basic Operators.- 2.3 The Stabilizing Solution.- 2.4 A Matrix Pencil Description.- 2.5 The Signature Condition.- Notes and References.- 3 H? Control: A Signature Condition Based Approach.- 3.1 Problem Statement.- 3.2 The Redheffer Theorem.- 3.3 A First Set of Necessary Solvability Conditions.- 3.4 A Second Set of Necessary Solvability Conditions.- 3.5 Coupled and Uncoupled Necessity Solvability Conditions.- 3.6 Sufficient Solvability Conditions: An Explicit Solution in KPYS Terms.- 3.7 Singular Problems: Necessary and Sufficient Conditions.- Notes and References.- 4 The Nehari Problem.- 4.1 The Two-Block Case.- 4.2 The One-Block Case.- Notes and References.- 5 Optimal H? Problems: A Singular Perturbation Approach.- 5.1 Optimal Solution of the H?- Control Problem.- 5.2 Case Studies.- Notes and References.- 6 Singular H? Problems.- 6.1 Robustness with Respect to Multiplicative Uncertainty.- 6.2 Sensitivity Minimization.- Notes and References.

'This is a useful book oriented to researchers, control systems engineers and applied mathematicians as well as to graduate students. Specialists in numerical computations will also find interesting issues in this book.' Mathematical Reviews

• 1 Linear Systems: Some Prerequisites.- 1.1 State Space Description and Input/Output Map.- 1.2 Dichotomy. RL?, RH+? and RH?? Spaces.- 1.3 Hankel and Toeplitz Operators.- 1.4 Balanced Forms.- Notes and References.- 2 The Kalman-Popov-Yakubovich System of Indefinite Sign.- 2.1 Popov Triplets: Associated Objects, Equivalence, Duality.- 2.2 Basic Operators.- 2.3 The Stabilizing Solution.- 2.4 A Matrix Pencil Description.- 2.5 The Signature Condition.- Notes and References.- 3 H? Control: A Signature Condition Based Approach.- 3.1 Problem Statement.- 3.2 The Redheffer Theorem.- 3.3 A First Set of Necessary Solvability Conditions.- 3.4 A Second Set of Necessary Solvability Conditions.- 3.5 Coupled and Uncoupled Necessity Solvability Conditions.- 3.6 Sufficient Solvability Conditions: An Explicit Solution in KPYS Terms.- 3.7 Singular Problems: Necessary and Sufficient Conditions.- Notes and References.- 4 The Nehari Problem.- 4.1 The Two-Block Case.- 4.2 The One-Block Case.- Notes and References.- 5 Optimal H? Problems: A Singular Perturbation Approach.- 5.1 Optimal Solution of the H?- Control Problem.- 5.2 Case Studies.- Notes and References.- 6 Singular H? Problems.- 6.1 Robustness with Respect to Multiplicative Uncertainty.- 6.2 Sensitivity Minimization.- Notes and References.

'This is a useful book oriented to researchers, control systems engineers and applied mathematicians as well as to graduate students. Specialists in numerical computations will also find interesting issues in this book.' Mathematical Reviews