CDS 131 | Linear Systems Theory

Winter 2025 | Instructor: Professor John Doyle

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Week 9

This week:

• Homework 9 (PDF) (Code) released (due 3/14)

All Announcements

Course Calendar

LN = Lecture Notes, CD = Callier & Desoer, Linear System Theory, DFT = Doyle, Francis, & Tannenbaum, Feedback Control Theory

Week 1 - Linear Dynamical Systems

• Homework 1: Linear Dynamical Systems (due 1/20, extended due to wildfires)

Dynamical Systems & State Space Models (Max)

1/6

(Boardwork) (Video)
Reading - LN 1, 2.1, CD 2.1, 5

Solutions of Linear, Time-Varying Systems (Max)

1/8

(Boardwork) (Video)
Reading - LN 2.2, CD 2.1

Week 2 - LTI and I/O Systems

• Homework 2: LTI and I/O Systems (due 1/21, extended due to holiday)

Solutions of Linear, Time-Invariant Systems (Max)

1/13

(Boardwork) (Video)
Reading - LN 2.3, CD 3, 4

Impulse Response & Transfer Functions (Max)

1/15

(Boardwork) (Video)
Reading - LN 2.4, CD Appendix C, D

Week 3 - Stability in State Space

• Recitation 1: Laplace & Z-Transforms (Boardwork) (Video)
• Homework 3: Transforms & Stability in State Space (due 1/27)

MLK Day, No Class

1/20

Reading - None!

Analytical Approaches to Stability (Max)

1/22

(Boardwork) (Video)
Reading - LN 3.1, CD 7.2

Week 4 - I/O Stability Theory

• Homework 4: Lyapunov & I/O Stability (due 2/3)

Invariance-Based Approaches to Stability (Max)

1/27

(Boardwork) (Video)
Reading - LN 3.2, CD 7.2

Norms on Signals & Systems (Max)

1/29

(Boardwork) (Video)
Reading - LN 3.3, DFT 2.1, 2.2

Week 5 - Controllability & Observability

• Homework 5: Controllability & Observability (due 2/10)

Controllability & Stabilizability (Max)

2/3

(Boardwork) (Video)
Reading - LN 4.1, CD 8

Observability, Detectability, & Realizations (Max)

2/5

(Boardwork) (Video)
Reading - LN 4.2, CD 8

Week 6 - Linear Control Design

• Homework 6: State & Output Feedback (due 2/19, extended due to holiday)

State & Output Feedback (Max)

2/10

(Boardwork) (Video)
Reading - LN 5.1

Optimal Control & Dynamic Programming (Max)

2/12

(Boardwork) (Video)
Reading - LN 5.2

Week 7 - The Linear Quadratic Regulator

• Homework 7: Linear Optimal Control (due 2/26)

President’s Day, No Class

2/17

Reading - None!

The LQR Problem (Max)

2/19

(Boardwork) (Video)
Reading - LN 5.3

Week 8 - The Feedback Loop & Parameterizations

• Homework 8: Feedback Systems & Internal Stability (due 3/5)

The Feedback Loop & Internal Stability (Max)

2/24

(Boardwork) (Video)
Reading - LN 5.4, DFT 3.1, 3.2

The Space of Stabilizing Controllers (Max)

2/26

(Boardwork) (Video)
Reading - LN 5.5, DFT 4, 5

Week 9 - System-Level Synthesis I

• Homework 9: System-Level Synthesis (PDF) (Code) (due 3/14)

The System-Level Parameterization (Lauren)

3/3

Reading - LN 5.6, DFT 4.1-4.3, ADLM 1

ADMM For System-Level Synthesis (Lauren)

3/5

Reading - LN 5.6, ADLM 2, 3

Week 10 - System-Level Synthesis II

Distributed Control with SLS (Lauren)

3/10

Reading - LN 5.6, ADLM 3

MPC & Infinite-Dimensional SLS (Lauren)

3/12

Reading - LN 5.6, ADLM 4