Notation and Symbols |
Elements of Linear System Theory / Chapter 1: |
Introduction / 1.1: |
State Description of Linear Systems / 1.2: |
State Description of Nonlinear and Linear Differential Systems / 1.2.1: |
Linearization / 1.2.2: |
Examples / 1.2.3: |
State Transformations / 1.2.4: |
Solution of the State Differential Equation of Linear Systems / 1.3: |
The Transition Matrix and the Impulse Response Matrix / 1.3.1: |
The Transition Matrix of a Time-Invariant System / 1.3.2: |
Diagonalization / 1.3.3: |
The Jordan Form / 1.3.4: |
Stability / 1.4: |
Definitions of Stability / 1.4.1: |
Stability of Time-Invariant Linear Systems / 1.4.2: |
Stable and Unstable Subspaces for Time-Invariant Linear Systems / 1.4.3: |
Investigation of the Stability of Nonlinear Systems through Linearization / 1.4.4: |
Transform Analysis of Time-Invariant Systems / 1.5: |
Solution of the State Differential Equation through Laplace Transformation / 1.5.1: |
Frequency Response / 1.5.2: |
Zeroes of Transfer Matrices / 1.5.3: |
Interconnections of Linear Systems / 1.5.4: |
Root Loci / 1.5.5: |
Controllability / 1.6: |
Definition of Controllability / 1.6.1: |
Controllability of Linear Time-Invariant Systems / 1.6.2: |
The Controllable Subspace / 1.6.3: |
Stabilizability / 1.6.4: |
Controllability of Time-Varying Linear Systems / 1.6.5: |
Reconstructibility / 1.7: |
Definition of Reconstructibility / 1.7.1: |
Reconstructibility of Linear Time-Invariant Systems / 1.7.2: |
The Unreconstructible Subspace / 1.7.3: |
Detectability / 1.7.4: |
Reconstructibility of Time-Varying Linear Systems / 1.7.5: |
Duality of Linear Systems / 1.8: |
Phase-Variable Canonical Forms / 1.9: |
Vector Stochastic Processes / 1.10: |
Definitions / 1.10.1: |
Power Spectral Density Matrices / 1.10.2: |
The Response of Linear Systems to Stochastic Inputs / 1.10.3: |
Quadratic Expressions / 1.10.4: |
The Response of Linear Differential Systems to White Noise / 1.11: |
White Noise / 1.11.1: |
Linear Differential Systems Driven by White Noise / 1.11.2: |
The Steady-State Variance Matrix for the Time-Invariant Case / 1.11.3: |
Modeling of Stochastic Processes / 1.11.4: |
Quadratic Integral Expressions / 1.11.5: |
Problems / 1.12: |
Analysis of Linear Control Systems / Chapter 2: |
The Formulation of Control Problems / 2.1: |
The Formulation of Tracking and Regulator Problems / 2.2.1: |
The Formulation of Terminal Control Problems / 2.2.3: |
Closed-Loop Controllers / 2.3: |
The Basic Design Objective |
The Stability of Control Systems / 2.4: |
The Steady-State Analysis of the Tracking Properties / 2.5: |
The Steady-State Mean Square Tracking Error and Input / 2.5.1: |
The Single-Input Single-Output Case / 2.5.2: |
The Multiinput Multioutput Case / 2.5.3: |
The Transient Analysis of the Tracking Properties / 2.6: |
The Effects of Disturbances in the Single-Input Single-Output Case / 2.7: |
The Effects of Observation Noise in the Single-Input Single-Output Case / 2.8: |
The Effect of Plant Parameter Uncertainty in the Single-Input Single-Output Case / 2.9: |
The Open-Loop Steady-State Equivalent Control Scheme / 2.10: |
Conclusions / 2.11: |
Optimal Linear State Feedback Control Systems / 2.12: |
Stability Improvement of Linear Systems by State Feedback / 3.1: |
Linear State Feedback Control / 3.2.1: |
Conditions for Pole Assignment and Stabilization / 3.2.2: |
The Deterministic Linear Optimal Regulator Problem / 3.3: |
Solution of the Regulator Problem / 3.3.1: |
Derivation of the Riccati Equation / 3.3.3: |
Steady-State Solution of the Deterministic Linear Optimal Regulator Problem / 3.4: |
Introduction and Summary of Main Results / 3.4.1: |
Steady-State Properties of Optimal Regulators / 3.4.2: |
Steady-State Properties of the Time-Invariant Optimal Regulator / 3.4.3: |
Solution of the Time-Invariant Regulator Problem by Diagonalization / 3.4.4: |
Numerical Solution of the Riccati Equation / 3.5: |
Direct Integration / 3.5.1: |
The Kalman-Englar Method / 3.5.2: |
Solution by Diagonalization / 3.5.3: |
Solution by the Newton-Raphson Method / 3.5.4: |
Stochastic Linear Optimal Regulator and Tracking Problems / 3.6: |
Regulator Problems with DisturbancesThe Stochastic Regulator Problem / 3.6.1: |
Stochastic Tracking Problems / 3.6.2: |
Solution of the Stochastic Linear Optimal Regulator Problem / 3.6.3: |
Regulators and Tracking Systems with Nonzero Set Points and Constant Disturbances / 3.7: |
Nonzero Set Points / 3.7.1: |
Constant Disturbances / 3.7.2: |
Asymptotic Properties of Time-Invariant Optimal Control Laws / 3.8: |
Asymptotic Behavior of the Optimal Closed-Loop Poles / 3.8.1: |
Asymptotic Properties of the Single-Input Single-Output Nonzero Set Point Regulator / 3.8.2: |
The Maximally Achievable Accuracy of Regulators and Tracking Systems / 3.8.3: |
Sensitivity of Linear State Feedback Control Systems / 3.9: |
Optimal Linear Reconstruction of the State / 3.10: |
Observers / 4.1: |
Full-Order Observers / 4.2.1: |
Conditions for Pole Assignment and Stabilization of Observers / 4.2.2: |
Reduced-Order Observers / 4.2.3: |
The Optimal Observer / 4.3: |
A Stochastic Approach to the Observer Problem / 4.3.1: |
The Nonsingular Optimal Observer Problem with Uncorretated State Excitation and Observation Noises / 4.3.2: |
The Nonsingular Optimal Observer Problem with Correlated State Excitation and Observation Noises / 4.3.3: |
The Time-Invariant Singular Optimal Observer Problem / 4.3.4: |
The Colored Noise Observation Problem / 4.3.5: |
Innovations / 4.3.6: |
The Duality of the Optimal Observer and the Optimal Regulator / 4.4: |
Steady-State Properties of the Optimal Observer |
The Duality of the Optimal Regulator and the Optimal Observer Problem / 4.4.1: |
Asymptotic Properties of Time-Invariant Steady-State Optimal Observers / 4.4.3: |
Optimal Linear Output Feedback Control Systems / 4.5: |
The Regulation of Linear Systems with Incomplete Measurements / 5.1: |
The Structure of Output Feedback Control Systems / 5.2.1: |
Conditions for Pole Assignment and Stabilization of Output Feedback Control Systems / 5.2.2: |
Optimal Linear Regulators with Incomplete and Noisy Measurements / 5.3: |
Problem Formulation and Solution / 5.3.1: |
Evaluation of the Performance of Optimal Output Feedback Regulators / 5.3.2: |
Proof of the Separation Principle / 5.3.3: |
Linear Optimal Tracking Systems with Incomplete and Noisy Measurements / 5.4: |
Sensitivity of Time-Invariant Optimal Linear Output Feedback Control Systems / 5.5: |
Linear Optimal Output Feedback Controllers of Reduced Dimensions / 5.7: |
Controllers of Reduced Dimensions / 5.7.1: |
Numerical Determination of Optimal Controllers of Reduced Dimensions / 5.7.3: |
Linear Optimal Control Theory for Discrete-Time Systems / 5.8: |
Theory of Linear Discrete-Time Systems / 6.1: |
State Description of Linear Discrete-Time Systems / 6.2.1: |
Interconnections of Discrete-Time and Continuous-Time Systems / 6.2.3: |
Solution of State Difference Equations / 6.2.4: |
Transform Analysis of Linear Discrete-Time Systems / 6.2.5: |
Duality / 6.2.7: |
Discrete-Time Vector Stochastic Processes / 6.2.10: |
Linear Discrete-Time Systems Driven by White Noise / 6.2.12: |
Analysis of Linear Discrete-Time Control Systems / 6.3: |
Discrete-Time Linear Control Systems / 6.3.1: |
The Steady-State and the Transient Analysis of the Tracking Properties / 6.3.3: |
Further Aspects of Linear Discrete-Time Control System Performance / 6.3.4: |
Optimal Linear Discrete-Time State Feedback Control Systems / 6.4: |
Stability Improvement by State Feedback / 6.4.1: |
The Linear Discrete-Time Optimal Regulator Problem / 6.4.3: |
Steady-State Solution of the Discrete-Time Regulator Problem / 6.4.4: |
The Stochastic Discrete-Time Linear Optimal Regulator / 6.4.5: |
Linear Discrete-Time Regulators with Non-zero Set Points and Constant Disturbances / 6.4.6: |
Sensitivity / 6.4.7: |
Optimal Linear Reconstruction of the State of Linear Discrete-Time Systems / 6.5: |
The Formulation of Linear Discrete- / 6.5.1: |
Notation and Symbols |
Elements of Linear System Theory / Chapter 1: |
Introduction / 1.1: |