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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.



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]


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
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
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
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
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
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
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
11/24 LTV Controllability and Observability Pages 176-180
11/25 State Feedback Pages 231-236
11/27 Thanksgiving Break -
11/30 TBA State feedback and simple tracking
12/1 Homework Assignment 8 due
12/2 Disturbances and integral control -
12/4 The Turbidostat and Simulink Simulink: Modeling
12/7 Observers 247-255
12/8 Design example Simulink: Full State Feedback, Observer / Controller co-design
12/9 Another design example m file, Simulink file
12/11 Homework Assignment 9 due + Future directions in control Example writeup, Future directions report, Example solutions


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