This course introduces basic concepts associated with the the "robustness analysis" approach to dynamical systems engineering, applicable to linear and nonlinear models. Topics include:

- Linear algebra and functional analysis background
- Models of general systems: behaviors, input/output maps, state space equations, transfer matrices, interconnections
- Basic system properties: stability, performance, linearity, time-invariance, causality, reachibility, observability
- Analysis and design in state space: Lyapunov functions, control Lyapunov functions, storage functions, Lyapunov equations, Riccati equations, Kalman-Yakubovich-Popov Lemma, balancing and balanced truncation, full state feedback, state observers, model-based controllers
- Analysis and design in input/output format: system norms, small gain theorem, generalized passivity, integral quadratic constraints, structured singular values, standard linear feedback optimization setup

- undergraduate linear systems (6.003)
- basic matrix analysis and linear algebra (18.06)

Lecture handouts and the text by Mohammed Dahleh, Munzer Dahleh, and George Verghese "Lectures on Dynamic Systems and Control" (a textbook-in-the-making posted on the Web chapter-wise).

**Megretski, Alexandre (Alex)**(Lecturer):- Room 32-D730,
Ext. 3-9828, email ameg@mit.edu
**Katsargyri, Georgia-Evangelia**(Teaching Assistant):- Room 32-D758,
Ext. 3-2832, email gkats@mit.edu
**Gaumond, Lisa**(Course Secretary):- Room 32-D733, Ext. 3-2184,
email lisaga@mit.edu

The URL for the 6.241 home page is

**http://web.mit.edu/6.241/www/index.html**

Lectures occur on Monday and Wednesday, 11am-12.30 pm, Room 4-231. Recitations will be held on Fridays, 2-3pm, Room 26-314.

Homework assignments will be posted on the class Web site on Wednesdays, due in class in one week (with few exceptions when the due time will be postponed because of tests or holidays). The homework will be corrected, graded, and returned as soon as possible. Solutions to the homework will be posted on the Web when the corrected homework is returned.

** Team work on home assignments is strictly encouraged, as far as
generating ideas and
arriving at the best possible solution is concerned. However, you have
to write your own comments and (if necessary for numerical
calculations) your own MATLAB code.
**

Some of the homework assignments will require the use of MATLAB, available with most of its toolboxes on Athena computers.

There will be two midterm exams (7.30-9.30pm on October 14 and November 18) and a final exam (exact time to be announced later). There will be no lectures on the days when midterm exams are given.

The letter grade will be determined at the end of the semester from a numerical grade N, obtained from the formula

N=0.2*H+0.25*Q1+0.25*Q2+0.3*F

where H is the average homework grade, Q1,Q2 are the midterm grades, and F is the final exam grade (H,Q1,Q2,F are numbers between 0 and 100). As a rule, a numerical grade above 80 means an "A", 75 to 80 means "A-", 70 to 75 means "B+", etc. For students near the boundaries, other factors may be taken into account to determine the letter grade, such as effort, classroom activity, etc.