General information

Catalog no.: 036012 (joint undergraduate/graduate)
Credit points: 3
Prerequisites: 035188—Control Theory
Grading policy: Homework (100%, 5 out of 6, provided all solutions are submitted)

Homework solutions to be submitted electronically in PDF format (typeset, not a scan of a handwritten text) to (if you're unlucky to be stuck with MSWord on Windows, instead of using LaTeX, PDF files can be created from DOC sources via this site for free)


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


Wednesday, 15:30-18:20, room 451, Lady Davis Bld.


  1. 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. Linear matrix equations
  2. Dynamical systems and transfer matrices
    1. Signals and systems in the time domain
    2. Transfer matrices of LTI systems (causality, stability, system norms)
    3. Rational transfer matrices (McMillan degree, poles, transmission zeros)
    4. Coprime factorization over H
  3. 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
  4. Classical single-loop control: review
  5. Generalized plant paradigm
    1. Weighted sensitivity problem
    2. Mixed sensitivity problem
    3. The "standard problem"
  6. System interconnections: linear fractional transformations
  7. Nominal stability & stabilization
    1. Internal stability and well posedness
    2. Stabilizability
    3. Stabilization (Youla parametrization of all stabilizing controllers)
  8. Model uncertainty and robustness
    1. Model uncertainties and their modeling
    2. Robust stability and stabilization
  9. Design method: H loop shaping
    1. MIMO loop shaping
    2. Robustness against normalized LCF uncertainty
    3. H loop shaping procedure


  1. Course lectures notes (password required)
  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. M. Green and 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.
    (available here)


  1. Introduction; mathematical background (also in beamer mode)
  2. Static systems, SVD (also in beamer mode) and chapter from notes (updated 8.11.2016)
  3. Signals, dynamic systems (kernel representation, state-space realizations) (also in beamer mode) (updated 10.11.2016)
  4. Systems in transformed domains; stability; system norms) (also in beamer mode)
  5. Rational transfer functions (poles, zeros, etc), coprime factorization: chapter from notes (password required)
  6. State-space realizations: basic properties: chapter from notes (password required)
  7. State-space realizations (contd)
  8. Model reduction via balanced truncation
  9. Optimization-based design & generalized plant (also in beamer mode) and: chapters from notes (password required)
  10. System interconnections; internal stability: chapter from notes (password required)
  11. Youla parametrization
  12. Youla parametrization (contd)
  13. H-inf loop shaping and robust stability (also in beamer mode)