# 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 ( |

## Lecturer

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

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

- Review of classical single-loop control
- Static systems: linear algebra revised
- Frozen-time signals and static systems: basic definitions
- Structural properties of static systems (kernel and image spaces, SVD, etc)
- Linear matrix equations

- Dynamical systems and transfer matrices
- Signals and systems in time and frequency domains
- Kernel representation of linear systems and their properties (causality, stability, time invariance)
- LTI systems in transformed domains (transfer functions, system norms)
- Coprime factorization over
`H-inf` - Real-rational transfer functions (McMillan degree, poles, transmission zeros)

- State-space realizations of transfer matrices
- Structural properties (controllability, observability, minimality, Kalman canonical decomposition)
- State-space machinery
- Model reduction by balanced truncation

- Generalized plant paradigm
- Weighted sensitivity problem
- Mixed sensitivity problem
- The "standard problem"

- System interconnections: linear fractional transformations
- Nominal stability & stabilization
- Internal stability and well posedness
- Stabilizability
- Stabilization (Youla parametrization of all stabilizing controllers)

- Model uncertainty and robustness
- Model uncertainties and their modeling
- Robust stability and stabilization

- Design method:
`H-inf`loop shaping

## Literature:

- Course lectures notes (last updated 31.1.2019)
- Skogestad, S. & I. Postlethwaite.
*Multivariable Feedback Control: Analysis and Design*, John Wiley & Sons, 1996. - Zhou, K., J. C. Doyle, & K. Glover.
*Robust and Optimal Control*, Prentice Hall, 1995. - M. Green and D. J. N Limebeer.
*Linear Robust Control*, Prentice Hall, Englewood Cliffs, 1995. - Doyle, J. C., B. A. Francis, & A. Tannenbaum.
*Feedback Control Theory*, MacMillan, 1992.

# Lectures

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

`H-inf`loop shaping (Chapter 9)

# Homework

- Homework assignment no. 1, submission deadline:
__Nov 14, 3:00pm__ - Homework assignment no. 2, submission deadline:
__Nov 28, 3:00pm__ - Homework assignment no. 3, submission deadline:
__Dec 11, 9:00pm__ - Homework assignment no. 4, submission deadline:
__Dec 25, 9:00pm__ - Homework assignment no. 5, submission deadline:
__Jan 8, 9:00pm__ - Homework assignment no. 6, submission deadline:
__Feb 5, 9:00pm__