General information

Catalog no.: 00360012 (joint undergraduate/graduate)
Credit points: 3
Prerequisites: 00350188—Control Theory
Grading policy: Homework (100%, average of 5 best out of 6, provided all solutions are submitted)

Homework solutions are to be submitted electronically in PDF format (typeset, not a scan of a handwritten text) to .

Lecturer

Leonid Mirkin, 210 D. Dan and Betty Kahn Bld., phone: 3149, email: 

Classes

Tuesday, 15:30-18:20, room 450, Lady Davis Bld.

Syllabus

  1. Review of classical single-loop control
  2. Static systems: linear algebra revised
    1. Frozen-time signals and static systems: basic definitions
    2. Structural properties of static systems (kernel and image spaces, SVD, etc)
  3. Dynamical systems and transfer functions
    1. Signals and systems in time and frequency domains
    2. LTI systems in transformed domains (transfer functions, system norms)
    3. Coprime factorization over H-inf
    4. Real-rational transfer functions (McMillan degree, poles, transmission zeros)
  4. State-space realizations of transfer matrices
    1. Structural properties (controllability, observability, minimality, Kalman canonical decomposition)
    2. State-space machinery
    3. Model reduction by balanced truncation
  5. Interactions between systems
    1. Basic interconnections and cancelations
    2. Linear fractional transformations
  6. Stability of interconnections
    1. Internal stability and well posedness
    2. Closed-loop stabilization and all stabilizing controllers (Youla-Kučera)
    3. Open-loop stabilization
  7. Performance via optimization methods
    1. The "standard problem"
    2. Weighted and mixed sensitivity problems
    3. Performance limitations
  8. Design method: H-inf loop shaping

Literature:

  1. Course lectures notes, updates
    • 15.6.2025: polished Thms. 6.5 and 6.6 and fixed typos in Remark 6.6 on pp. 127–128
    • 25.6.2025: polished §6.1.3
  2. Skogestad, S. & I. Postlethwaite. Multivariable Feedback Control: Analysis and Design, John Wiley & Sons, 1996.
  3. Zhou, K., J. C. Doyle, & K. Glover. Robust and Optimal Control, Prentice Hall, 1995.
  4. Green, M. & D. J. N Limebeer. Linear Robust Control, Prentice Hall, Englewood Cliffs, 1995.
  5. Doyle, J. C., B. A. Francis, & A. Tannenbaum. Feedback Control Theory, MacMillan, 1992.

Lectures

  1. Chapter 1 (also in beamer mode)
  2. Chapter 2 (also in beamer mode)
  3. Chapter 3 (also in beamer mode)
  4. Chapter 4 (also in beamer mode)
  5. Chapter 5 (also in beamer mode)
  6. Chapter 6 (also in beamer mode)

Homework