6.241 Dynamic Systems and Control
Lecture 4: Singular Values
Readings: DDV, Chapter 4
Emilio Frazzoli
Aeronautics and Astronautics
Massachusetts Institute of Technology
February 14, 2011
E. Frazzoli (MIT)
Lecture 4: Singular Values
Feb 14, 2011
1/9
Outlin
6.241 Dynamic Systems and Control
Lecture 3: Least Square Solutions of Linear Problems
Readings: DDV, Chapter 3
Emilio Frazzoli
Aeronautics and Astronautics
Massachusetts Institute of Technology
February 9, 2011
E. Frazzoli (MIT)
Lecture 3: Least Squares
6.241 Dynamic Systems and Control
Lecture 2: Least Square Estimation
Readings: DDV, Chapter 2
Emilio Frazzoli
Aeronautics and Astronautics
Massachusetts Institute of Technology
February 7, 2011
E. Frazzoli (MIT)
Lecture 2: Least Squares Estimation
Feb 7,
6.241 Dynamic Systems and Control
Lecture 1: Introduction, linear algebra review
Readings: DDV, Chapter 1
Emilio Frazzoli
Aeronautics and Astronautics
Massachusetts Institute of Technology
February 2, 2011
E. Frazzoli (MIT)
Lecture 1: Introduction
Feb 2,
6.241 Spring 2011
Final Exam
5/16/2011, 9:00am 12:00pm
The test is open books/notes, but no collaboration is allowed: i.e., you should not
discuss this exam or solution approaches with anybody, except for the teaching sta.
Problem 1
Let (A, b, c, 0) be a
6.241 Spring 2011
Midterm Exam
March 27, 2011
Problem 1
Let A Cnn , and B Cmm . Show that X (t) = eAt X (0)eBt is the solution to X =
AX + X B .
1
Solution Recalling the denition of matrix exponential, eAt = i! (At)i , it is
i=0
clear that, for any matrix
6.241 Spring 2011
Midterm Exam
3/16/2011
You have a total of three hours to complete this exam. These three hours can be chosen
at your convenience.
Problem 1
Let A Cnn , and B Cmm . Show that X (t) = eAt X (0)eBt is the solution to X =
AX + X B .
Problem
6.241 Dynamic Systems and Control
Lecture 25: H Synthesis
Emilio Frazzoli
Aeronautics and Astronautics
Massachusetts Institute of Technology
May 11, 2011
E. Frazzoli (MIT)
Lecture 25: H Synthesis
May 11, 2011
1 / 12
Standard setup
Consider the following s
6.241 Dynamic Systems and Control
Lecture 24: H2 Synthesis
Emilio Frazzoli
Aeronautics and Astronautics
Massachusetts Institute of Technology
May 4, 2011
E. Frazzoli (MIT)
Lecture 24: H2 Synthesis
May 4, 2011
1 / 27
Standard setup
Consider the following s
6.241 Dynamic Systems and Control
Lecture 23: Feedback Stabilization
Readings: DDV, Chapter 28
Emilio Frazzoli
Aeronautics and Astronautics
Massachusetts Institute of Technology
May 2, 2011
E. Frazzoli (MIT)
Lecture 23: Feedback Stabilization
May 2, 2011
6.241 Dynamic Systems and Control
Lecture 22: Balanced Realization
Readings: DDV, Chapter 26
Emilio Frazzoli
Aeronautics and Astronautics
Massachusetts Institute of Technology
April 27, 2011
E. Frazzoli (MIT)
Lecture 22: Balanced Realization
April 27, 201
6.241 Dynamic Systems and Control
Lecture 21: Minimal Realizations
Readings: DDV, Chapters 25
Emilio Frazzoli
Aeronautics and Astronautics
Massachusetts Institute of Technology
April 25, 2011
E. Frazzoli (MIT)
Lecture 21: Minimal Realizations
April 25, 20
6.241 Dynamic Systems and Control
Lecture 20: Reachability and Observability
Readings: DDV, Chapters 23, 24
Emilio Frazzoli
Aeronautics and Astronautics
Massachusetts Institute of Technology
April 20, 2011
E. Frazzoli (MIT)
Lecture 20: Reachability and Ob
6.241 Dynamic Systems and Control
Lecture 17: Robust Stability
Readings: DDV, Chapters 19, 20
Emilio Frazzoli
Aeronautics and Astronautics
Massachusetts Institute of Technology
April 6, 2011
E. Frazzoli (MIT)
Lecture 17: Robust Stability
April 6, 2011
1 /
6.241 Dynamic Systems and Control
Lecture 16: Bodes Sensitivity Integral
Readings: DDV, Chapter 18
Emilio Frazzoli
Aeronautics and Astronautics
Massachusetts Institute of Technology
April 4, 2011
E. Frazzoli (MIT)
Lecture 16: Bode Integral
April 4, 2011
1
6.241 Dynamic Systems and Control
Lecture 13: I/O Stability
Readings: DDV, Chapters 15, 16
Emilio Frazzoli
Aeronautics and Astronautics
Massachusetts Institute of Technology
March 14, 2011
E. Frazzoli (MIT)
Lecture 13: I/O Stability
Mar 14, 2011
1/6
L2 -i
6.241 Dynamic Systems and Control
Lecture 12: I/O Stability
Readings: DDV, Chapters 15, 16
Emilio Frazzoli
Aeronautics and Astronautics
Massachusetts Institute of Technology
March 14, 2011
E. Frazzoli (MIT)
Lecture 12: I/O Stability
Mar 14, 2011
1 / 12
In
6.241 Dynamic Systems and Control
Lecture 9: Transfer Functions
Readings: DDV, Chapters 10, 11, 12
Emilio Frazzoli
Aeronautics and Astronautics
Massachusetts Institute of Technology
March 2, 2011
E. Frazzoli (MIT)
Lecture 9: Transfer Functions
Mar 2, 2011
6.241 Dynamic Systems and Control
Lecture 8: Solutions of State-space Models
Readings: DDV, Chapters 10, 11, 12 (skip the parts on transform methods)
Emilio Frazzoli
Aeronautics and Astronautics
Massachusetts Institute of Technology
February 28, 2011
E. F
6.241 Dynamic Systems and Control
Lecture 7: State-space Models
Readings: DDV, Chapters 7,8
Emilio Frazzoli
Aeronautics and Astronautics
Massachusetts Institute of Technology
February 25, 2011
E. Frazzoli (MIT)
Lecture 7: State-space Models
Feb 25, 2011
1
6.241 Dynamic Systems and Control
Lecture 6: Dynamical Systems
Readings: DDV, Chapter 6
Emilio Frazzoli
Aeronautics and Astronautics
Massachusetts Institute of Technology
February 23, 2011
E. Frazzoli (MIT)
Lecture 6: Dynamical Systems
Feb 23, 2011
1 / 10
6.241 Dynamic Systems and Control
Lecture 5: Matrix Perturbations
Readings: DDV, Chapter 5
Emilio Frazzoli
Aeronautics and Astronautics
Massachusetts Institute of Technology
February 16, 2011
E. Frazzoli (MIT)
Lecture 5: Matrix Perturbations
Feb 16, 2011