6.241J | Spring 2011 | Graduate

Dynamic Systems and Control


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).

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

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 H2 optimization  
24 H optimization  
Learning Resource Types
Problem Sets with Solutions
Lecture Notes
Online Textbook