Course Details

ELE 701 Linear System Theory
2020-2021 Spring 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 09/03/2021.


Course Name Code Semester Theory
Credit ECTS
LINEAR SYSTEM THEORY ELE701 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 objectiveMany engineering problems can be analyzed and solved within the framework of system concept, which is a very fundamental notion in engineering. It is possible to classify systems into two main groups as liner and nonlinear although they may have many different properties and characteristics. Systems can be assumed as linear under certain conditions despite the fact that most of the systems are nonlinear. In this way, linear systems point of view can also be used in the analysis of nonlinear systems. In this course, the aim is to provide the necessary background for the students to be able to understand and solve the engineering problems by using the theory and methods developed for linear systems. 
Learning outcomes
  1. A student completing the course successfully is expected to
  2. L.O.1. understand the system concept.
  3. L.O.2. be able to obtain linear models for physical systems.
  4. L.O.3. be aware of diferences and discrepancies between the actual system and its linear model.
  5. L.O.4. fully understand and analyse such systems.
  6. L.O.5. have the adequate knowledge to follow further studies involving system concept.
Course ContentLinear spaces. Change of basis. Linear operators. Range space and null space. Eigenvalues and eigenvectors. Jordan form representation. Function of a square matrix. Norms. Linear system description: input-output and state variable descriptions, time invariant and time varying systems. Modal decomposition. Equivalent (or similar) systems and equivalence (or similarity) transformation. Linear system analysis: controllability, observability and stability. 
References1. Chen C.T., Linear System Theory and Design, HRW, 1984.
2. Kailath T., Linear Systems, Prentice Hall, 1980.
3. Decarlo R.A., Linear Systems: A state variable approach with numerical
implementation, Prentice Hall, 1989.
4. Rugh W.J., Linear System Theory, 2nd Ed., Prentice Hall, 1996.
5. Brogan W.L., Modern Control Theory, 3rd Ed., Prentice Hall, 1991.

Course outline weekly

Week 1Linear spaces : field, linear space, subspace, span, linear independence, dimension, basis, change of basis.
Week 2Linear oprerators and representations of a linear operator.
Week 3Linear operators: range and null spaces, eigenvalues and eigenvectors, Jordan form representation.
Week 4Polynomial of a square matrix, minimal polynomial, function of a square matrix, norms and inner product.
Week 5Linear system description: input-output approach (for both time-invariant and time varying).
Week 6Linear system description: state variable approach (for both time-invariant and time varying).
Week 7Solution of dynamical equations, fundamental martix and state transition matrix.
Week 8Solution of dynamical equation, computation of eAt and (SI-A)-1, Faddeev algorithm, modal decomposition.
Week 9Equivalent (or similar) systems and equivalence (or similarity) transformation.
Week 10Midterm Exam
Week 11 Linear system analysis: Controllability and observability.
Week 12 Linear system analysis: Controllability and observability.
Week 13 Linear system analysis: Stability.
Week 14 Linear system analysis: Stability.
Week 15Final exam
Week 16Final exam

Assesment methods

Course activitiesNumberPercentage
Field activities00
Specific practical training00
Final exam150
Percentage of semester activities contributing grade succes050
Percentage of final exam contributing grade succes050

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 assignment6636
Midterms (Study duration)12525
Final Exam (Study duration) 13030
Total Workload3573256

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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