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. 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. Linear matrix equations
  3. Dynamical systems and transfer matrices
    1. Signals and systems in time and frequency domains
    2. Kernel representation of linear systems and their properties (causality, stability, time invariance)
    3. LTI systems in transformed domains (transfer functions, system norms)
    4. Coprime factorization over H-inf
    5. 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. 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-inf loop shaping


  1. Course lectures notes (last updated 31.1.2019)
  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.


  1. Introduction; mathematical background (also in beamer mode)
  2. Review of SISO control; static systems, SVD (also in beamer mode) (updated 6.11.2018)
  3. Block matrices, linear matrix equations; discrete signals and dynamic systems (insight) (also in beamer mode)
  4. Systems in time and transformed domains) (also in beamer mode)
  5. Coprime factorization; real-rational transfer functions (poles, zeros, etc) (also in beamer mode) (updated 27.11.2018)
  6. State-space realizations: structural properties; Gilbert's realization from notes (also in beamer mode)
  7. State-space machinery; model reduction via balanced truncation (also in beamer mode) (updated 18.12.2018)
  8. More on pole directions (§4.3.2); computing Hinf norm (§4.3.3); interactions between systems (Ch. 5)
  9. Feedback stability and stabilization (§§6.1.1-6.1.4)
  10. More on stabilization (Chapter 6 from §6.1.5 and up)
  11. The standard problem (Chapter 7)
  12. The standard problem (Chapter 7, §7.3.2 and up)
  13. H-inf  loop shaping (Chapter 9)