Documentation Table of Contents

1. Getting Started

• Using the Package for the First Time
• Structure of the Application
• Robustness of Numerical Methods

2. Introduction

• Quick Reference
• Solutions of the Lyapunov and Sylvester Matrix Equations
• Solutions of the Algebraic Riccati Equations
• Reduction to Controller-Hessenberg and Observer-Hessenberg Forms
• Controllability and Observability Tests
• Pole Assignment
• Feedback Stabilization
• Design of the Reduced-Order State Estimator (Observer)
• Model Reduction
• Model Identification
• Miscellaneous Matrix Decompositions and Functions
• An Industrial Application: Controlling the Drum Boiler
• The State-Space Model of a Drum Boiler
• System Responses, Stability, and Poles
• Testing the Controllability
• The Design of the LQR (linear quadratic regulation) Controller
• The Controller Design Using Constrained Feedback Stabilization
• The Observer Design

3. Matrix Equations and Control Applications

• Lyapunov Equations
• Riccati Equations
• The Schur Methods for the Riccati Equations
• The Inverse-Free Generalized Eigenvector and Schur Methods for the Riccati Equations
• The Matrix Sign-Function Methods for the Riccati Equations
• The Newton Methods for the Riccati Equations
• LQR and LQG (linear quadratic Gaussian) Designs Using Riccati Equations

4. Block Hessenberg Forms

• Controller-Hessenberg Forms
• Observer-Hessenberg Forms
• Controllability and Observability Tests Using Block Hessenberg Forms

5. Pole Assignment and Stabilization by State Feedback

• Pole Assignment Methods
• The Recursive Algorithms
• The Explicit and Implicit QR Algorithms
• The Schur Method
• Partial Pole Assignment
• Constrained Feedback Stabilization
• Lyapunov Feedback Stabilization

6. State Estimation

• Full-Order State Estimation
• Reduced-Order State Estimator
• Reduced-Order State Estimator via Pole Assignment
• Reduced-Order State Estimator via Sylvester-Observer Equation

7. Model Reduction

• Cholesky Factors of the Controllability and Observability Gramians
• Model Reduction Using Schur and Square-Root Methods

8. Model Identification

• Time-Domain System Identification
• Identification Using Markov Parameters
• Identification Using Input-Output Data (Subspace System Identification Method)
• Frequency Domain System Identification

9. Generalized Eigenvalue Problem

• Generalized Eigenvalue Problem
• Generalized Schur Decomposition

Appendix. Collection of Control Systems for Case Studies

• Continuous-Time Models
• The Absorption Column
• The F-8 Aircraft
• The L-1011 Aircraft
• The Tubular Ammonia Reactor
• The Fluid Catalytic Reactor
• The Binary Distillation Column
• The Drum Boiler
• The Flight Control System
• The Automobile Gas Turbine
• The CH-47 Helicopter
• The Magnetic Tape
• The Electric Power System
• The J-100 Jet Engine
• The "Smart" Highway
• The Generator Axle in a Power Plant
• Discrete-Time Models
• The Catalytic Cracker
• The Chemical Plant
• The Paper Machine
• The Steam Power System