Course Details

ELE 754 Nonlinear Systems
2021-2022 Fall term information

The course is not open this term

Timing data are obtained using weekly schedule program tables. To make sure whether the course is cancelled or time-shifted for a specific week one should consult the supervisor and/or follow the announcements.

Course definition tables are extracted from the ECTS Course Catalog web site of Hacettepe University ( in real-time and displayed here. Please check the appropriate page on the original site against any technical problems. Course data last updated on 21/10/2021.


Course Name Code Semester Theory
Credit ECTS
NONLINEAR SYSTEMS ELE754 Any Semester/Year 3 0 3 10
Course languageTurkish
Course typeElective 
Mode of DeliveryFace-to-Face 
Learning and teaching strategiesLecture
Question and Answer
Problem Solving
Instructor (s)Department Faculty 
Course objectiveIn practice many systems are nonlinear. The objective of the course is to provide necessary background to understand, analyze and control such systems. These include nonlinear models and nonlinear phenomena; second-order systems, phase portraits; some fundamental properties of nonlinear state equations such as existence, uniqueness; stability analysis (Lyapunov, input-output, passivity); frequency domain analysis; controller design methods for nonlinear systems such as feedback linearization and sliding-mode control. 
Learning outcomes
  1. A student completing the course successfully is expected to
  2. L.O.1. understand the nature of nonlinear systems.
  3. L.O.2. be aware of difficulties involving nonlinear systems.
  4. L.O.3. be able to use some techniques to analyse nonlinear systems.
  5. L.O.4. be able to use some techniques to design controllers for nonlinear systems.
  6. L.O.5. have a suitable background to follow further studies in nonlinear systems and control.
Course ContentIntroduction to nonlinear systems and some examples. Second order systems and phase plane. Lyapunov stability. Input-output stability. Passivity. Frequency domain analysis: absolute stability, circle criterion, Popov criterion, describing function method . Nonlinear control systems design: feedback linearization and sliding-mode control.  
References1. Khalil H. K., Nonlinear Systems, 3rd Ed., Prentice Hall, 2002.
2. Slotine J. J. E. and Li W., Applied Nonlinear Control, Prentice Hall, 1991.
3. Ýsidori A., Nonlinear Control Systems, 3rd Ed., Fall/ Springer, 1995.
4. Vidyasagar M., Nonlinear Systems Analysis, 2nd Ed., Prentice Hall, 1993.
5. Sastry S., Nonlinear Systems: Analysis, Stability and Control, Fall/ Springer-Verlag, 1999.

Course outline weekly

Week 1Nonlinear models and nonlinear phenomena and some example systems. Lienard?s equation, Van der Pol equation.
Week 2Second order systems, phase plane, multiple Equilibria.
Week 3Qualitative behavior near equilibrium points, limit cycles, existence of periodic orbits, Poincare-Bendixson criterion, Bendixson criterion, bifurcation.
Week 4Solution of nonlinear state equations, existence and uniqueness, Lipschitz condition, continuous dependence on initial conditions and parameters, differentiability of solutions and sensitivity equations.
Week 5Lyapunov stability: autonomous systems.
Week 6Lyapunov stability: the invariance principle, linearization and local stability, comparision functions.
Week 7Lyapunov stability: nonautonomous systems, boundedness and ultimate boundedness, input-to- state stability.
Week 8Input-output stability.
Week 9Passivity.
Week 10Midterm Exam.
Week 11Frequency domain analysis of feedback systems: absolute stability, circle criterion, Popov criterion.
Week 12Frequency domain analysis of feedback systems: describing functionmethod .
Week 13Feedback linearization.
Week 14Sliding mode control.
Week 15Preparation for the final exam.
Week 16Final exam.

Assesment methods

Course activitiesNumberPercentage
Field activities00
Specific practical training00
Final exam140
Percentage of semester activities contributing grade succes060
Percentage of final exam contributing grade succes040

Workload and ECTS calculation

Activities Number Duration (hour) Total Work Load
Course Duration (x14) 13 3 39
Laboratory 0 0 0
Specific practical training000
Field activities000
Study Hours Out of Class (Preliminary work, reinforcement, ect)149126
Presentation / Seminar Preparation000
Homework assignment6848
Midterms (Study duration)12525
Final Exam (Study duration) 12525
Total Workload3570263

Matrix Of The Course Learning Outcomes Versus Program Outcomes

D.9. Key Learning OutcomesContrubition level*
1. Has highest level of knowledge in certain areas of Electrical and Electronics Engineering.    X
2. Has knowledge, skills and and competence to develop novel approaches in science and technology.    X
3. Follows the scientific literature, and the developments in his/her field, critically analyze, synthesize, interpret and apply them effectively in his/her research.   X 
4. Can independently carry out all stages of a novel research project.  X  
5. Designs, plans and manages novel research projects; can lead multidisiplinary projects.  X  
6. Contributes to the science and technology literature.  X  
7. Can present his/her ideas and works in written and oral forms effectively; in Turkish or English.  X  
8. Is aware of his/her social responsibilities, evaluates scientific and technological developments with impartiality and ethical responsibility and disseminates them.  X  

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

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