# 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

- 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 the time domain
- Transfer matrices of LTI systems (causality, stability, system norms)
- Rational transfer matrices (McMillan degree, poles, transmission zeros)
- Coprime factorization over
`H`_{∞}

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

- Classical single-loop control: review
- 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`loop shaping_{∞}- MIMO loop shaping
- Robustness against normalized LCF uncertainty
`H`loop shaping procedure_{∞}

## Literature:

- Course lectures notes (password required)
- 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.

(available here)

# Lectures

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

# Homework

- Homework assignment no. 1, submission deadline:
__Nov 16, 3:00pm__ - Homework assignment no. 2, submission deadline:
__Dec 1, 11:00am__ - Homework assignment no. 3, submission deadline:
__Dec 14, 3:00pm__ - Homework assignment no. 4, submission deadline:
__Dec 26, 11:59pm__ - Homework assignment no. 5, submission deadline:
__Jan 11, 3:00pm__ - Homework assignment no. 6, submission deadline:
__Feb 15, 3:00pm__

## Software:

- Weighted sensitivity solver (requires LMI-toolbox). Use "
`help wsens`" to see usage instructions. - Mixed sensitivity solver (requires LMI-toolbox). Use "
`help msens`" to see usage instructions.