ECE 2646: Linear
System Theory (3 Credits, Fall 2008)
Description: Linear spaces and operators, mathematical
descriptions of linear systems, controllability and observability,
irreducible realization of rational transfer-function matrices, canonical
forms, state feedback and state estimators, and stability.
Prerequisite: Knowledge of linear algebra, differential equations,
and feedback control systems (ECE 1673, notes are available at http://www.engr.pitt.edu/electrical/faculty-staff/mao/1673/).
Time: Wednesday 5:20 pm-7:50 pm.
Instructor: Dr. Zhi-Hong Mao, (office) 434 Benedum
Hall, (phone) 412-624-9674, (email) maozh@engr.pitt.edu,
(office hours) Tuesday 4 pm-7 pm.
TA: Mr. Mir
H. Mahmood, (email) mhm16@pitt.edu.
Text: Chi-Tsong Chen, Linear
System Theory and Design, 3rd Edition, Oxford University Press, Oxford, UK,
1999.
Course Evaluation: Homework and class participation 35%, midterm exam
30%, and final exam 35%.
Tentative schedule for lectures
(notes will be available at http://www.engr.pitt.edu/electrical/faculty-staff/mao/2646/
):
|
Date |
Topic |
|
|
Week 1 (8/27) |
Lecture
1: Course organization and introduction; review of classical control;
review of linear algebra (I) |
Chapter 1 |
|
Week 2 (9/3) |
Lecture
2: Mathematical description of systems |
Sections 2.1-2.3 and Lecture
2 from ECE 1673 |
|
Week 3 (9/10) |
Lecture
3: Rational transfer functions and state-space equations; linearization;
review of linear algebra (II) |
Sections 2.3, 2.4, 3.1-3.4,
3.5 (not including |
|
Week 4 (9/17) |
Lecture
4: Review of linear algebra (III); solution to LTI state equations |
Sections 4.1 and 4.2 (not
including discretization) |
|
Week 5 (9/24) |
Lecture
5: State-space solutions and realizations |
Sections 4.3 (not including
4.3.1 and 4.3.2) and 4.4 |
|
Week 6 (10/1) |
Lecture
6: State-space realizations and stability |
Sections 5.1, 5.2 (not
including 5.2.1), and 5.3 (not including 5.3.1) |
|
Week 7 (10/8) |
Lecture
7: Controllability |
Sections 6.1 and 6.2 |
|
Week 8 (10/15) |
Midterm |
|
|
Week 9 (10/22) |
Lecture 8: Observability; canonical decomposition |
Sections 6.3 and 6.4 |
|
Week 10 (10/29) |
Lecture 9: Coprimeness; minimal realizations of transfer functions |
Sections 7.1 and 7.2 |
|
Week 11 (11/5) |
Lecture 10: Minimal
realizations of transfer matrices; pole placement |
Sections 7.6 and 7.7 |
|
Week 12 (11/12) |
Lecture 11: State feedback |
Sections 8.1, 8.2, and 8.3
(not including 8.3.1 and 8.3.2) |
|
Week 13 (11/19) |
Lecture 12: State estimator
|
|
|
Week 14 (11/26) |
No class (Thanksgiving
recess) |
Sections 8.4 and 8.5 |
|
Week 15 (12/3) |
Review of classes |
|
|
Week 16 (12/10) |
Final exam |
|