System Analysis

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This course develops the mathematical techniques for the analysis of systems in the time domain. An introduction to state space concepts and coordinate transformations is given, followed by solutions to state space equations and advanced topics such as controllability and observability. This course is very mathematical, but real-world examples will be given to bridge the gap between theory and practice.


TEXT: “Linear System Theory and Design,” Third Edition, by C.-T. Cheng, Oxford University Press, New York, NY, 1999.


  • State Space Modeling
    • Matrix representation
    • Definitions and Connections
    • Similarity Transformations
    • Jordan-Block Form
    • Multi-Input-Multi-Output Systems
    • Transmission Zeros
  • Linear Dynamical Equations
    • Solution of a Dynamical Equation
    • Impulse Response Matrices
    • Forced and Unforced Systems
    • Transition Matrix Properties
  • Stability of Linear Systems
    • Bounded-Input-Bounded-Output Stability
    • Asymptotic Stability
    • Lyapunov Stability Criterion
  • Controllability and Observability
    • Control and Observer Canonical Forms
    • Feedback Structures
    • Linear Systems Analysis
    • Controllability and Observability Grammians
  • Linearization of Systems
    • Superposition Concepts
  • Advanced Topics (time permitting)
    • Discrete-Time Systems
    • Control Issues
    • System Realizations


Years Taught: Fall '12, Fall '11, Fall '10, Fall '09, Fall '08, Fall '07, Fall '06, Fall '05, Fall '04, Fall '03, Fall '02, Fall '01