This section contains course notes and a schedule of readings for each lecture.
Course Notes
Course notes are courtesy of Mohammed Dahleh, Munther A. Dahleh, and George Verghese, and are used with permission. Chapters 9, 16 and 23 are not available on MIT OpenCourseWare.
The full set of course notes are also available as one file (PDF - 10.3MB).
CHAPTER # | TOPICS | FILES |
---|---|---|
1 | Linear algebra review | (PDF) |
2 | Least squares estimation | (PDF) |
3 | Least squares solution of y = < A, x > | (PDF) |
4 | Matrix norms and singular value decomposition | (PDF) |
5 | Matrix perturbations | (PDF) |
6 | Dynamic models | (PDF) |
7 | State-space models | (PDF) |
8 | Simulation/realization | (PDF) |
9 | [topic not available] | |
10 | Discrete-time linear state-space models | (PDF) |
11 | Continuous-time linear state-space models | (PDF) |
12 | Modal decomposition of state-space models | (PDF) |
13 | Internal (Lyapunov) stability | (PDF) |
14 | Internal stability for LTI systems | (PDF) |
15 | External input-output stability | (PDF) |
16 | System norms | |
17 | Interconnected systems and feedback: well-posedness, stability, and performance | (PDF) |
18 | Performance of feedback systems | (PDF) |
19 | Robust stability in SISO systems | (PDF) |
20 | Stability robustness | (PDF) |
21 | Robust performance and introduction to the structured singular value function | (PDF) |
22 | Reachability of DT LTI systems | (PDF) |
23 | CT reachability, canonical forms | |
24 | Observability | (PDF) |
25 | Minimal state-space realization | (PDF) |
26 | Balanced realization | (PDF) |
27 | Poles and zeros of MIMO systems | (PDF) |
28 | Stabilization: state feedback | (PDF) |
29 | Observers, model-based controllers | (PDF) |
30 | Minimality and stability of interconnected systems | (PDF) |
Schedule of Readings
LEC # | LECTURE TOPICS | READINGS |
---|---|---|
1 | Introduction to dynamic systems and control, matrix algebra | Chapter 1 |
2 | Least squares error solutions of overdetermined / underdetermined systems | Chapters 2 and 3 |
3 | Matrix norms, SVD, matrix perturbations | Chapter 4 |
4 | Matrix perturbations | Chapter 5 |
5 | State-space models, linearity and time invariance | Chapters 6–8 |
6 | Solutions of state-space models | Chapters 10 and 11 |
7 | Similarity transformations, modes of LTI systems, Laplace transform, transfer functions | Chapter 12 |
8 | Stability, Lyapunov methods | Chapters 13 and 14 |
9 | External I/O stability, storage functions | Chapter 15 |
10 | Interconnected systems, feedback, I/O stability | Chapters 15 and 17 |
11 | System norms | Chapter 16 |
12 | Performance measures in feedback control | Chapter 18 |
13 | Small gain theorem, stability robustness | Chapter 19 |
14 | Stability robustness (MIMO) | Chapters 20 and 21 |
15 | Reachability | Chapter 22 |
16 | Reachability: standard and canonical forms, modal tests | Chapter 23 |
17 | Observability | Chapter 24 |
18 | Minimality, realization, Kalman decomposition, model reduction | Chapter 25 |
19 | State feedback, observers, output feedback, MIMO poles and zeros | Chapters 26–29 |
20 | Minimality of interconnections, pole/zero cancellations | Chapter 30 |
21 | Parameterization of all stabilizing controllers | |
22 | Optimal control synthesis: problem setup | |
23 | H_{2} optimization | |
24 | H_{∞} optimization |