# Nonlinear Systems (EE612) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Nonlinear Systems EE612 Area Elective 3 0 0 3 5
Pre-requisite Course(s)
A prior differential equations, linear systems and/or a basic control systems course is strongly recommended.
Course Language English Elective Courses Ph.D. . Prof. Dr. Reşat Özgür DORUK Teaching of advanced concepts in nonlinear system theory to aid the graduate students mastering in dynamical systems theory, control, power systems, neural networks and theoretical neuroscience. The students who succeeded in this course; Explain nonlinear phenomena Distinguish linear and nonlinear systems Describe equilibrium concept Analyze local system behaviour around equilibrium Assess stability of a nonlinear system both locally and globally. Assess the stability of a general system by Lyapunov methods. Define and determine the existence of a limit cycle Analyze advanced nonlinear phenomena such as bifurcations. Nonlinear models and nonlinear phenomena, qualitative behaviour of second order systems, Lyapunov stability, passivity, Poincaré and Bendixon theorems, frequency response of nonlinear systems and describing functions, applications of Lyapunov theory, advanced nonlinear phenomena such as bifurcations.

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Nonlinear Phenomena: Linear and Nonlinear Systems
2 Equilibrium Points, Jacobian Linearization
3 Analysişs of second order systems in phase plane
4 Behaviour of system trajectories in the vicinity of equilibrium points. Local stability.
5 Stability in general, types of stability and Lyapunov methods
6 Applications of Lyapunov Stability I
7 Applications of Lyapunov Stability II
8 MIDTERM EXAM-I
9 Limit cycles, Poincare and Bendixon theorems
10 Frequency response and describing functions.
11 Advanced Nonlinear Phenomena: Bifurcations
12 Bifurcation in one dimensional systems
13 Bifurcation in two dimensional systems (generalizations to large order cases)
14 Bifurcation analysis approaches (MATCONT Package)
15 Bifurcation Control Approaches
16 MIDTERM EXAM-II

### Sources

Course Book 1. Khalil, Hassan K. "Noninear systems." Prentice-Hall, New Jersey 2.5 (1996) 2. Vidyasagar, Mathukumalli. Nonlinear systems analysis. Vol. 42. Siam, 2002. 3. 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 30
Final Exam/Final Jury 1 40
Toplam 3 70
Percentage of Semester Work 100 100

### 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 apply knowledge on Mathematics, Science and Engineering to advanced systems. X
2 Implementing long-term research and development studies in the major fields 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.
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.

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 16 5 80
Presentation/Seminar Prepration
Project
Report
Homework Assignments
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 3 6
Prepration of Final Exams/Final Jury 1 5 5