State Variables for Engineers
ECE 601

This is a graduate-level course on linear dynamical systems with an emphasis on state-space modeling in both discrete and continuous time. Topics covered include equilibrium points and linearization, natural and forced responses, canonical forms and transformations, controllability and observability, and control-theoretic concepts such as pole placement, stabilization, dynamic compensation, and the separation principle. The material in this course is fundamental knowledge for students pursuing research in systems/control theory, signal processing, or mechanical/electrical/industrial engineering.

    1. Fundamentals
      1. Introduction
      2. State-space models
      3. Modeling electrical circuits
      4. Modeling mechanical systems
      5. Numerical simulation and phase diagrams
      6. Linearization
    2. LTI Systems
      1. LTI system models
      2. State transformations
      3. System response
      4. Diagonalization
      5. Jordan form
    3. Analysis
      1. BIBO stability
      2. Lyapunov stability
      3. Controllability
      4. Observability
      5. Minimality and the transient response
    4. Control
      1. Static state feedback
      2. Steady-state tracking
      3. Observers
      4. Separation principle
      5. Linear-quadratic regulator
      6. Kalman filter
      7. Linear-quadratic-Guassian control