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Linear Systems Theory
Instructor: Eric Klavins
M, T, W, F 1130a - 1230p
Office Hours:

• Klavins, CSE 236, Friday 1230p-230p
• Wu, Sieg 126A, Tuesday 3:30p-5:00p; Friday 9:00a-10:20a

Loew 216

Text: Linear System Theory and Design by Chen. 3rd Edition.

Contents 1 Description 2 Homework Grade 3 EDGE students 4 Schedule

Description

Linearity, linearization, finite dimensionality, time-varying vs. time-invariant linear systems, interconnection of linear systems, functional/structural descriptions of linear systems, system zeros and invertibility, linear system stability, system norms, state transition, matrix exponentials, controllability and observability, realization theory. Complete syllabus here.

Homework Grade

Homework will be graded on a scale of 10, each homework assignment has equal weight when merged into the final course grade.
Graded homework will be returned on the next Monday in class.

EDGE students

The graded homework will be scanned and emailed to EDGE students by the UW EDGE office. To help the UW EDGE office return your graded homework in time, please try to submit your homework through the EDGE system if possible; if you cannot submit through the EDGE system and email your homework to the TA or Professor Klavins, please put your name and email address on the front page of your homework. Your homework grade can also be accessed from [1]

Schedule

Date	Topic	Reading
9/30	Introduction and Course Overview	Pages 1-4
10/2	I/O Systems and Basic Definitions	Pages 5-8
10/5	Homework Assignment 1 due	Solution [2]
10/6	Impulse Response, Time Invariance, Transfer Functions and State Space	Pages 8-16
10/7	Linearization, Examples, Discrete Time	Pages 17-37
10/9	Linear Algebra: Basis, Systems of Linear Equations, Rank, Singularity	Pages 44-53
10/12	Homework Assignment 2 due	Solution [3]
10/13	Linear Algebra: Basis, Systems of Linear Equations, Rank, Singularity	Pages 44-53
10/14	Linear Algebra: Similarity, Jordan Form	Pages 53-61, Notes on Jordan form
10/16	Linear Algebra: Matrix Exponentials	Pages 61-70
10/19	Homework Assignment 3 due	Solution [4]
10/20	Solutions to linear ODEs using matrix exponentials	Pages 67-71, 86-90
10/21	The Caley-Hamilton Theorem	Pages 61-67
10/23	Quadratic Forms	Pages 70-73
10/26	Homework Assignment 4 due	Solution [5]
10/27	Solutions to state space equations	Pages 86-90, 106-110
10/28	Time varying systems	Pages 106-112
10/30	BIBO Stability and Internal Stability	Pages 121-126
11/2	Homework Assignment 5 due	Solution [6]
11/3	More Internal Stability and The Lyapunov Theorem	Pages 132-135
11/4	The Lyapunov Theorem and Local Stability	Pages 132-135
11/6	MIDTERM	Through 11/2
11/9	Discussion of the MIDTERM solutions	-
11/10	Controllability	Pages 143-150
11/11	Veteran's Day	-
11/13	Controllability Indices	Pages 150-152
11/16	Homework Assignment 6 due	Mathematica Code
11/17	Observability	Pages 153-158
11/18	Canonical Decomposition	Pages 158-164
11/20	No Class Friday: Makeup session to be scehduled	-
11/23	Homework Assignment 7 due	-

Exams:

• Midterm: Tentative Date: Nov. 6
• Final Exam: Wednesday, Dec. 16, 230-420 pm, LOW 216