Stabilization of Linear Systems

1. Introduction.- 1.1 Stability Concepts: The Problem of Stabilization.- 1.2 Linear Systems with Constant Coefficients: The Theorem on Stability by the Linear Approximation.- 1.3 An Overview of Some Stabilization Problems.- Notes and References.- 2. Stabilization of Linear Systems.- 2.1 Controllability.- 2.2 Stabilizability: Stabilization Algorithms.- 2.3 Observability and Detectability: State Estimators: A Parametrization of Stabilizing Controllers.- 2.4 Liapunov Equations.- 2.5 Optimal Stabilization of Linear Systems: The Kalman-Lurie-Yakubovich-Popov Equations.- 2.5.1 Statement of the Problem.- 2.5.2 The Case of Stable Matrix A.- 2.5.3 The Case When (A, B) Is Stabilizable.- 2.6 Estimate of the Cost Associated with a Stabilizing Feedback Control: Loss in Performance Due to the Use of a Dynamic Controller.- 2.7 Stabilization with Disturbance Attenuation.- 2.7.1 Input-Output Operators.- 2.7.2 Disturbance Attenuation by State Feedback.- Notes and References.- 3. Stabilization of Linear Systems with Two Time Scales.- 3.1 Separation of Time Scales.- 3.2 Controllability and Stabilizability.- 3.3 State Estimators.- 3.4 Optimal Stabilization for Systems with Two Time Scales.- 3.4.1 Statement of the Problem.- 3.4.2 The Asymptotic Structure of the Optimal Cost.- 3.4.3 Suboptimal Stabilization of Systems with Two Time Scales.- Notes and References.- 4. High-Gain Feedback Stabilization of Linear Systems.- 4.1 An Example.- 4.2 Square Systems with Minimum Phase.- 4.3 Invariant Zeros of a Linear System.- 4.4 Systems with Stable Invariant Zeros and with rank CB = rank C = p.- 4.5 High-Gain Feedback Stabilization of Linear Systems with Higher Relative Degree.- 4.6 The Special Popov Form of Linear Systems.- 4.7 High-Gain Stabilization of Linear Systems: The General Case.- Notes and References.- 5. Adaptive Stabilization and Identification.- 5.1 Adaptive Stabilization in the Fundamental Case.- 5.2 Adaptive Stabilization in the Case of Unmodeled Fast Dynamics.- 5.3 Asymptotic Structure of the Invariant Zeros of a System with Two Time Scales and Adaptive Stabilization.- 5.4 Adaptive Stabilization of Some Linear Systems of Relative Degree Two.- 5.5 An Algorithm of Adaptive Identification.- Notes and References.- 6. Discrete Implementation of Stabilization Procedures.- 6.1 Discrete Time Implementation of a State Feedback Control.- 6.2 Discrete-Time Implementation of a Stabilizing Dynamic Controller.- 6.3 Performance Estimates.- 6.4 Discrete Implementation of a Linear Feedback Control for Systems with Two Time Scales.- 6.5 Discrete Implementation of a High-Gain Feedback Control.- 6.6 Discrete Implementation of the Adaptive Stabilization Algorithm.- Notes and References.