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Tables of Contents for Stabilization of Linear Systems
Chapter/Section Title
Page #
Page Count
Preface
xi
Notations and Terminology
xii
Introduction
1
18
Stability Concepts: The Problem of Stabilization
2
3
Linear Systems with Constant Coefficients: The Theorem on Stability by the Linear Approximation
5
8
An Overview of Some Stabilization Problems
13
6
Notes and References
18
1
Stabilization of Linear Systems
19
72
Controllability
19
6
Stabilizability: Stabilization Algorithms
25
11
Observability and Detectability: State Estimators: A Parametrization of Stabilizing Controllers
36
4
Liapunov Equations
40
3
Optimal Stabilization of Linear Systems: The Kalman-Lurie-Yakubovich-Popov Equations
43
37
Statement of the Problem
43
2
The Case of Stable Matrix A
45
15
The Case When (A, B) Is Stabilizable
60
20
Estimate of the Cost Associated with a Stabilizing Feedback Control: Loss in Performance Due to the Use of a Dynamic Controller
80
4
Stabilization with Disturbance Attenuation
84
7
Input-Output Operators
84
4
Disturbance-Attenuation by State Feedback
88
1
Notes and References
89
2
Stabilization of Linear Systems with Two Time Scales
91
42
Separation of Time Scales
92
4
Controllability and Stabilizability
96
6
State Estimators
102
7
Optimal Stabilization for Systems with Two Time Scales
109
24
Statement of the Problem
109
3
The Asymptotic Structure of the Optimal Cost
112
11
Suboptimal Stabilization of Systems with Two Time Scales
123
9
Notes and References
132
1
High-Gain Feedback Stabilization of Linear Systems
133
68
An Example
133
1
Square Systems with Minimum Phase
134
7
Invariant Zeros of a Linear System
141
3
Systems with Stable Invariant Zeros and with rank CB = rank C = p
144
6
High-Gain Feedback Stabilization of Linear Systems with Higher Relative Degree
150
21
The Special Popov Form of Linear Systems
171
16
High-Gain Stabilization of Linear Systems: The General Case
187
14
Notes and References
199
2
Adaptive Stabilization and Identification
201
42
Adaptive Stabilization in the Fundamental Case
201
6
Adaptive Stabilization in the Case of Unmodeled Fast Dynamics
207
6
Asymptotic Structure of the Invariant Zeros of a System with Two Time Scales and Adaptive Stabilization
213
15
Adaptive Stabilization of Some Linear Systems of Relative Degree Two
228
5
An Algorithm of Adaptive Identification
233
10
Notes and References
241
2
Discrete Implementation of Stabilization Procedures
243
58
Discrete Time Implementation of a State Feedback Control
244
12
Discrete-Time Implementation of a Stabilizing Dynamic Controller
256
10
Performance Estimates
266
10
Discrete Implementation of a Linear Feedback Control for Systems with Two Time Scales
276
14
Discrete Implementation of a High-Gain Feedback Control
290
5
Discrete Implementation of the Adaptive Stabilization Algorithm
295
6
Notes and References
299
2
Bibliography
301
6
Index
307