Linear System Theory (EE503) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Linear System Theory EE503 3 0 0 3 5
Pre-requisite Course(s)
A prior differential equations, signals and systems and/or a basic control systems course is strongly recommended.
Course Language English
Course Type N/A
Course Level Natural & Applied Sciences Master's Degree
Mode of Delivery Face To Face
Learning and Teaching Strategies Lecture, Discussion, Question and Answer, Drill and Practice.
Course Coordinator
Course Lecturer(s)
  • Prof. Dr. Reşat Özgür DORUK
Course Assistants
Course Objectives Teaching of advanced concepts in linear system theory to aid the graduate students mastering in signal processing, dynamical systems theory and control.
Course Learning Outcomes The students who succeeded in this course;
  • Explain the general system concepts
  • Distinguish linear and nonlinear systems
  • Describe different linear system representations
  • Model and analyze the systems represented in state space form.
  • Design state feedback controllers
  • Design state observers
  • Deal with the difficulties observed in controller and observer designs.
  • Learn new topics in system theory based on the material covered in this course in their possible future studies
Course Content Review of linear algebra concepts, linear system representations, existence of solutions, state transition matrices, canonical realizations, controller designs, observer designs, introduction to multi-input multi-output systems.

Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Review of Linear Algebra Concepts: Linear Spaces, Basis Vectors, Linear Transformations Glance this week’s topics from the lecture
2 Linear system representations: Frequency domain, transfer functions and state space. Transformations between frequency domain and state space. Review last week and Glance this week’s topics from the lecture
3 Linear Operators: Range and Null Spaces, Eigenvalues, Eigenvectors, Cayley-Hamilton theorems Review last week and Glance this week’s topics from the lecture
4 Canonical Forms: Diagonal and Jordan Canonical forms. Various cases. Review last week and Glance this week’s topics from the lecture
5 Solution of linear dynamical systems equations. State Transition Matrix concept. Review last week and Glance this week’s topics from the lecture
6 Methods of derivation and computation of state transition matrices. Review last week and Glance this week’s topics from the lecture
7 Connections to nonlinear systems, linearization, equilibrium concepts. Review last week and Glance this week’s topics from the lecture
8 MIDTERM EXAM-I Review all topics up to the current week
9 Stability: Stability definitions, local stability, global stability, asymptotic stability, stability in the sense of Lyapunov, stability analysis of systems in frequency domain or state space. Review last week and Glance this week’s topics from the lecture
10 Controllability and Observability Review last week and Glance this week’s topics from the lecture
11 Controllable and Observable Canonical Forms. Controller and Observer Designs Review last week and Glance this week’s topics from the lecture
12 Issues associated with Controllability and Observability Review last week and Glance this week’s topics from the lecture
13 Minimal Realizations and Kalman Decomposition Review last week and Glance this week’s topics from the lecture
14 Pole Placement State Feedback Review last week and Glance this week’s topics from the lecture
15 Introduction to Multi-Input and Multiple- Output (MIMO) systems Review last week and Glance this week’s topics from the lecture
16 MIDTERM EXAM-II Review all topics

Sources

Course Book 1. CALLIER, Frank M.; DESOER, C. A. Linear System Theory (Springer Texts in Electrical Engineering). 1991.
2. ANTSAKLIS, Panos J.; MICHEL, Anthony N. Linear systems. Boston, MA: Birkhäuser, 2006.
3. PANOS J. ANTSAKLIS; ANTHONY N. MICHEL. A Linear Systems Primer. Springer, 2007.
Other Sources 4. Öğretim Elemanı Taafından Sağlanacak Belgeler/Instructor Notes

Evaluation System

Requirements Number Percentage of Grade
Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments - -
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 50
Final Exam/Final Jury 1 35
Toplam 3 85
Percentage of Semester Work 65
Percentage of Final Work 35
Total 100

Course Category

Core Courses X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Ability to apply knowledge on Mathematics, Science and Engineering to advanced systems. X
2 Implementing long-term research and development studies in major areas of Electrical and Electronics Engineering. X
3 Ability to use modern engineering tools, techniques and facilities in design and other engineering applications. X
4 Graduating researchers active on innovation and entrepreneurship.
5 Ability to report and present research results effectively.
6 Increasing the performance on accessing information resources and on following recent developments in science and technology. X
7 An understanding of professional and ethical responsibility.
8 Increasing the performance on effective communications in both Turkish and English.
9 Increasing the performance on project management.
10 Ability to work successfully at project teams in interdisciplinary fields. X

ECTS/Workload Table

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours) 16 3 48
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 14 3 42
Presentation/Seminar Prepration
Project
Report
Homework Assignments
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 10 20
Prepration of Final Exams/Final Jury 1 20 20
Total Workload 130