ECE 2646: Linear
System Theory (3 Credits, Fall 2009)
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 6:00 pm-8:30 pm.
Instructor: Dr. Zhi-Hong Mao, (office) 434 Benedum
Hall, (phone) 412-624-9674, (email) maozh@engr.pitt.edu,
(office hours) Tuesday 4 pm-6 pm.
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 (9/2) |
Lecture
1: Course organization and introduction; review of classical control;
review of linear algebra (I) |
Chapter 1 |
|
Week 2 (9/9) |
Lecture
2: Mathematical description of systems |
Sections 2.1-2.3 and Lecture
2 from ECE 1673 |
|
Week 3 (9/16) |
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 (9/23) |
Lecture
4: Review of linear algebra (III); solution to LTI state equations |
Sections 4.1 and 4.2 (not
including discretization) |
|
Week 5 (9/30) |
Lecture
5: State-space solutions and realizations |
Sections 4.3 (not including
4.3.1 and 4.3.2) and 4.4 |
|
Week 6 (10/7) |
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 (10/14) |
Lecture
7: Controllability |
Sections 6.1 and 6.2 |
|
Week 8 (10/21) |
Midterm |
|
|
Week 9 (10/28) |
Lecture
8: Observability; canonical decomposition |
Sections 6.3 and 6.4 |
|
Week 10 (11/4) |
Lecture
9: Coprimeness; minimal realizations of
transfer functions |
Sections 7.1 and 7.2 |
|
Week 11 (11/11) |
Lecture
10: Minimal realizations of transfer matrices; pole placement |
Sections 7.6 and 7.7 |
|
Week 12 (11/18) |
Lecture
11: State feedback |
Sections 8.1, 8.2, and 8.3
(not including 8.3.1 and 8.3.2) |
|
Week 13 (11/25) |
No class (Thanksgiving
recess) |
|
|
Week 14 (12/2) |
Lecture 12: State estimator |
Sections 8.4 and 8.5 |
|
Week 15 (12/9) |
Review of classes |
|
|
Week 16 (12/16) |
Final exam |
|