# Linear System Theory (EE503) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Linear System Theory EE503 Area Elective 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 Elective Courses Ph.D. Face To Face Lecture, Discussion, Question and Answer, Drill and Practice. Prof. Dr. Reşat Özgür DORUK Teaching of advanced concepts in linear system theory to aid the graduate students mastering in signal processing, dynamical systems theory and control. 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 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. 4. Öğretim Elemanı Taafından Sağlanacak Belgeler/Instructor Notes

### Evaluation System

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 35 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Ability to carry out advanced research activities, both individual and as a member of a team
2 Ability to evaluate research topics and comment with scientific reasoning
3 Ability to initiate and create new methodologies, implement them on novel research areas and topics
4 Ability to produce experimental and/or analytical data in systematic manner, discuss and evaluate data to lead scintific conclusions
5 Ability to apply scientific philosophy on analysis, modelling and design of engineering systems
6 Ability to synthesis available knowledge on his/her domain to initiate, to carry, complete and present novel research at international level
7 Contribute scientific and technological advancements on engineering domain of his/her interest area
8 Contribute industrial and scientific advancements to improve the society through research activities

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