Multivariable Control Theory | MAE 6780

Silvia Ferrari
Sibley School of Mechanical and Aerospace Engineering
Cornell University

Course Synopsis

Introduction to multivariable feedback control theory in both time and frequency domain. Topics include model-based control, optimal control and estimation, H-infinity and robust control, multi-objective control synthesis via convex optimization, and adaptive model reference control. Prerequisites/Corequisites: MAE 4780 or MAE 5780, ECE 5210 or permission of instructor; strong background in classical control, linear algebra, and state space models.

Course Outline

    • Introduction and Motivation
      System and control terminology
      Multivariable control scope and applications
      From modern to post-modern control methods
    • Modeling Dynamic Systems for Control
      Continuous-time systems
      Discrete-time systems
      Case studies in mechanical, electro-mechanical, and aerospace systems
    • Dynamic System Representation and Analysis
      State-space form and transfer function matrix
      Transition matrix approach
      Controllability and observability
      Case studies in mechanical and aerospace systems
    • Optimal Control and Estimation
      Optimality conditions
      Hamilton-Jacobi-Bellman equation
      Optimal state estimation and duality
      Case studies in implicit-model following and LQG
    • Robust Control
      H-infinity standard plant and design
      Input-output stability
      LMI and IQC theory and terminology
      Multi-objective synthesis
    • Adaptive Control
      Gain scheduling
      Model-reference adaptive systems (MRAS)
      The MIT rule
      MRAS design via Lyapunov theory
    • Independent Project
      Model predictive control
      Sliding model control
      Feedback linearization
      Applications in aerospace and automotive engineering

Principal References

Available at the Cornell University Library

Required Textbooks:

  • Bernard Friedland, Control System Design: An Introduction to
    State-Space Methods
    , Dover, Mineola, NY, 2005.
  • Katsuhiko Ogata, MATLAB for Control Engineers, Prentice Hall, NJ, 2008.

Supplementary References:

  1. H. K. Khalil, Nonlinear Systems, Third Ed., Prentice Hall, 2002.
  2. R. F. Stengel, Optimal Control and Estimation, Dover Publications, 1994.
  3. D. E. Kirk, Optimal Control Theory; an Introduction, Prentice-Hall, 1970.
  4. R. A. Hyde, H-infinity Aerospace Control Design: A VSTOL Flight Application, Advances in Industrial Control, Springer, 1995.
  5. K. J. Astrom and B. Wittenmark, Adaptive Control, II Edition, Addison Wesley, 1995.
  6. R. J. Vanderbei, Linear Programming: Foundations and Extensions, Kluwer, 1997.
  7. Gilbert Strang, Linear Algebra and its Applications, Academic Press, NY, 1980.
  8. Michael D. Greenberg, Advanced Engineering Mathematics,
    Prentice-Hall, NJ, 1998.

Office Hours

  • Silvia Ferrari, Room 543 Upson Hall, Monday and Wednesday, 1:00-3:00 p.m.

    Additional information are posted on the Cornell University Blackboard site, available at:

    For any other questions, contact Prof. Ferrari or the Teaching Assistants.

    Last updated on January 20, 2018, by