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525.466 - Linear System Theory Course Homepage

Instructor Information

Alan Pue

Work Phone: (443) 778-6503

Course Information

Course Description

This course covers the structure and properties of linear dynamic systems with an emphasis on the single-input, single-output case. Topics include the notion of state-space, state variable equations, review of matrix theory, linear vector spaces, eigenvalues and eigenvectors, the state transition matrix and solution of linear differential equations, internal and external system descriptions, properties of controllability and observability and their applications to minimal realizations, state-feedback controllers, asymptotic observers, and compensator design using state-space and transfer function methods. An introduction to multi-input, multi-output systems is also included, as well as the solution and properties of time-varying systems.

Prerequisites

Courses in matrix theory and linear differential equations.

Course Goal

Obtain a fundamental understanding of the structure, solution, and characteristics of both linear algebraic and linear dynamic systems

Course Objectives

  • Provide a common basis through state-space and transfer function methods for the analysis and design of dynamic systems that are described by linear differential equations, i.e.. the same form of equations may apply to a tractor-trailor or a jet aircraft.


  • Understand the characteristics and structural properties of linear dynamic systems:

    • time solution
    • frequency domain description
    • stability
    • controllability and observability

  • Understand the relationships betwen input-ouput behavior and internal (state) descriptions

  • Utilize this knowledge to alter the behavior of a system in a useful way

    • controller and observer design
    • theoretical limitations and constraints in design

When This Course is Typically Offered

Odd year Fall terms at APL

Syllabus

Topics Covered

  • Properties of Linear Systems
  • State Equations
  • Linear Vector Spaces
  • Linear Algebraic Equations
  • Eigenvalues and Eigenvectors, Jordan Form
  • Solution of State-Space Equations
  • System Stability
  • Controllability and Observability
  • Minimal Realizations
  • State Feedback
  • State Observers
  • Controller-Observer Compensator Design
  • Discrete Time and Time-Varying Systems
  • Multivariable Systems

Student Assessment Criteria

2 Quizzes 30%
Final Exam 30%
Homework 40%

All homework is due within one week of its assignment. Late homework will not be accepted without the prior permission of the instructor.

Textbooks

Textbook information for this course is available online through the MBS Direct Virtual Bookstore.

Course Notes

There are notes for this course.

Final Words from the Instructor

Course provides an essential understanding of linear system theory which is fundamental to many applications in control, communications, and signal processing

(Last Modified: 07-23-2009 at 3:33:09 PM)