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Stabilization of Linear Systems

One of the main problems in control theory is the stabilization problem consisting of finding a feedback control law ensuring stability; when the linear approximation is considered, the nat­ ural problem is stabilization of a linear system by linear state feedback or by using a linear dynamic contro...

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Bibliographic Details
Main Authors: Dragan, Vasile, Halanay, Aristide (Author)
Format: eBook
Language:English
Published: Boston, MA Birkhäuser 1999, 1999
Edition:1st ed. 1999
Series:Systems & Control: Foundations & Applications
Subjects:
Control Theory
Systems Theory, Control
System Theory
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 3.4 Optimal Stabilization for 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
  • 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
  • 2.6 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
  • 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

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