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

Reading

 

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 Jordan form), and 3.6

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