**EEE 582**

**Linear
Systems**

**Fall
2014**

TTh 12:00-1:15, CDS13

**Instructor: Kostas Tsakalis, GWC
358, 965-1467, **

This page: http://tsakalis.faculty.asu.edu/

**Textbook: **Chen, Linear System Theory and Design,Oxford

**Course Outline:**

- Linear algebra review; Least-squares problems, singular
value decomposition
- State-space concepts; description of dynamical systems,
basic properties
- State Transition Matrix
- Stability
- Controllability-Observability
- Realizability, Minimal Realizations
- Canonical Forms
- Pole-Placement design of controllers and observers

**Grading:** HW 15%, 2 Midterms 50% total (drop worst score), Final 35%

Absolute
Grading Scale: A > 85 > B > 70 > C > 50 > ... E

(Cut-off
points may decrease depending on the final grade distribution.)

Grade distribution after the 5^{th}
test

**ALL
TESTS ARE CLOSED-BOOKS/NOTES. One sheet of formulae allowed. **

**Final Exam:** Tue, Dec 9, 12:10-14:00

**Academic integrity policy:**

**https://provost.asu.edu/index.php?q=academicintegrity**

**HW
Assignments, Notes**

Notes: Linear Algebra, Stability/Controllability/Observability

Examples of Observers
and Integrator Augmentation

Solved Problems

HW#1, Due 9/11 SOLUTIONS

Problems
1, 2, 3, 4 from the linked file EEE582 Homework Problems

EEE 582, Test 1, 9/18. Material: HW#1 SOLUTIONS

Basic Definitions, System Models, Linearization, Continuous/Discrete-time
systems.

HW#2, Due 9/25 SOLUTIONS

Problems
5, 6, 7, 8, 9, from the linked file EEE582 Homework Problems

EEE
582, Test 2, 10/2. Material: HW#2 SOLUTIONS

Linear Algebra review, Jordan forms, SVD

HW#3 Due 10/9 SOLUTIONS

Problems
10-18 from the linked file EEE582
Homework Problems

EEE 582, Test 3, 10/16. Material: HW#3 SOLUTIONS

Matrix exponential, Solution of State equations, Stability

HW#4 Due 10/30 SOLUTIONS

Problems
19-24 from the linked file EEE582
Homework Problems

EEE
582, Test 4, 11/6. Material: HW#4 SOLUTIONS

Controllability, Observability

HW#5 Due
11/13 SOLUTIONS

Problems
25-32 from the linked file EEE582
Homework Problems

EEE 582, Test 5, 11/20. Material: HW#5 SOLUTIONS

Realization Theory, Canonical forms (Kalman, Observable, Controllable, Balanced)

HW#6 Due 12/2 SOLUTIONS

State Feedback , State Estimation,
Observers, Output Feedback, Separation Principle

Problems
33-39 from the linked file EEE582
Homework Problems

HW # Minimal
Realization using Matlab

Consider the 2 x 2 6th order system defined by appending the tranfer functions of each input to each output:

H_11(s) = 1/(s+1), H_12(s) = 1/(s+1)+1/(s+2), H_21(s) = 1/(s+2), H_22(s)
= 1/[(s+1)(s+2)]

1. Use the Kalman canonical decomposition theorem
(see notes) to compute a minimal realization of this system

2. Use balanced truncation to compute reduced order models of orders 2 and 3
and use Bode plots/step responses to analyze the reduction error.

HW #SVD: See linked m-file, answer questions at the end