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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 |

# 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 | |

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 |

Exams:

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