EE 212 Linear System Theory

Course description

Theory and application of discrete and continuous-time linear dynamical systems. Review of applied linear algebra; least-norm and least-squares methods. Autonomous linear dynamical systems; interpretations of eigenvalues, eigenvectors, matrix exponential, and invariant sets. Singular value decomposition with applications. Linear dynamical systems with inputs and outputs; transfer matrices. Observability and state estimation; controllability and state transfer. Examples and applications from digital filters, circuits, signal processing, and control systems.
Prerequisite : EEE 35 or equivalent and Math 114 or equivalent

Course objectives

At the end of this course, the student should be able :
To analyze any general linear system. To compute solutions to state equations. To derive appropriate inputs to
drive a linear system to convergence in a specified time. To observe the states of the system from the system output(s).

Text

Any graduate linear system theory text.

References

B.C. Kuo. Automatic Control Systems, 5th edition.
D'Azzo and Houpis. Linear Control System Analysis and Design :
Conventional and Modern, 3rd edition.
R.C. Dorf. Modern Control Systems, 6th edition.
Shahian and Rasul. Control System Design Using Matlab.

Grading

2 long exams     50 %
homeworks     20 %
lab exercises     30 %

Grading scale

92 - 100    1.0
88 - < 92    1.25
84 - < 88    1.5
80 - < 84    1.75
76 - < 80    2.0
72 - < 76    2.25
68 - < 72    2.5
64 - < 68    2.75
60 - < 64    3.0
< 60           5.0

Course outline

I. Class policies
A. Class requirements / expectations
B. Possible class projects

II. Overview
    A. How do we classify systems
    B. Concept of a state
    C. Some examples

III. Linear functions
A. Examples and applications
B. Linearization

IV. Lumped state-space models
    A. Simple pendulum, RLC circuit, mechanical system
    B. State-space models from ODEs
    C. Canonical forms

V. Linear algebra review
A. Orthonormal vectors and QR factorization
B. Least-squares method

VI. Autonomous linear systems

VII. Quadratic forms and SVD

VIII. Controllability and state transfer

IX. State-feedback

X. Observability and state estimation

XI. Feedback observer design and observer-based controller design

Lecture notes and homeworks

lecture 00
lecture 01
lecture 02
hw 01
lecture 03
hw 02
lecture 04
hw 03
lecture 05
lecture 06
lecture 07
lecture 08
hw 04
lecture 09