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EEC252 – Multivariable Control System Design

3 units – Winter Quarter

Lecture: 3 hours

Prerequisite: EEC 250

Grading: Letter; homework, design and exams.

Catalog Description:

Review of single-loop feedback design. Stability, performance and robustness of multivariable control systems. LQG design. H-infinity design. Frequency response methods. Optimization-based design.

Expanded Course Description:

To equip students in modern control system design, theory, and techniques for future careers in research and industry.

  1. Review of Single-Loop Feedback Design
    1. Design objectives, stability, performance
    2. Plant uncertainty, robustness, gain and phase margins
    3. Feedback, controller structure
    4. Limitations on performance, right half-plane poles and zeros
    5. Youla parametrization for single-loop systems
  2. Stability, Preformance and Robustness of Multivariable Control Systems
    1. Stability criteria
    2. Singular values, performance criteria
    3. Plant uncertainty
    4. Robust stability
    5. Robust performance
  3. LQG Design
    1. Solution to LQG problem
    2. Performance and robustness of optimal state feedback
    3. Effect of observer; loop transfer recovery
    4. Right half-plane zeros
    5. Design example
  4. H-infinity Design
    1. H-infinity formulation of design problem
    2. Youla parametrization
    3. Solution of the H-infinity problem
    4. The Hankel Approximation problem
    5. Design example
  5. Frequency Response Methods
    1. Diagonal Dominance
    2. Nyquist and inverse Nyquist array
    3. Design procedure
  6. Optimization Based Design
    1. Formulation of design objectives as optimization problem
    2. Convex optimization
    3. Nonconvex optimization
    4. Design procedure


  1. J. M. Maciejowski, Multivariable Feedback Design, Addison-Wesley, 1989.

Instructors: Mayne, Wang


Last revised: November 1989