# Department of Electrical and Electronics Engineering

Course Details

#### ELE 601 Linear System Theory2019-2020 Summer 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 (http://akts.hacettepe.edu.tr) in real-time and displayed here. Please check the appropriate page on the original site against any technical problems. Course data last updated on 07/08/2020.

ELE601 - LINEAR SYSTEM THEORY

Course Name Code Semester Theory
(hours/week)
Application
(hours/week)
Credit ECTS
LINEAR SYSTEM THEORY ELE601 Any Semester/Year 3 0 3 8
Prerequisite(s)None
Course languageTurkish
Course typeElective
Mode of DeliveryFace-to-Face
Learning and teaching strategiesLecture
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

WeeksTopics
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 14Linear system analysis: Stability.
Week 15Final exam
Week 16Final exam

Assesment methods

Course activitiesNumberPercentage
Attendance00
Laboratory00
Application00
Field activities00
Specific practical training00
Assignments610
Presentation00
Project00
Seminar00
Midterms140
Final exam150
Total100
Percentage of semester activities contributing grade succes050
Percentage of final exam contributing grade succes050
Total100

Activities Number Duration (hour) Total Work Load
Course Duration (x14) 13 3 39
Laboratory 0 0 0
Application000
Specific practical training000
Field activities000
Study Hours Out of Class (Preliminary work, reinforcement, ect)14570
Presentation / Seminar Preparation000
Project000
Homework assignment6636
Midterms (Study duration)12525
Final Exam (Study duration) 13030

Matrix Of The Course Learning Outcomes Versus Program Outcomes

D.9. Key Learning OutcomesContrubition level*
12345
1. Has general and detailed knowledge in certain areas of Electrical and Electronics Engineering in addition to the required fundamental knowledge.    X
2. Solves complex engineering problems which require high level of analysis and synthesis skills using theoretical and experimental knowledge in mathematics, sciences and Electrical and Electronics Engineering.    X
3. Follows and interprets scientific literature and uses them efficiently for the solution of engineering problems.  X
4. Designs and runs research projects, analyzes and interprets the results.  X
5. Designs, plans, and manages high level research projects; leads multidiciplinary projects.  X
6. Produces novel solutions for problems.  X
7. Can analyze and interpret complex or missing data and use this skill in multidiciplinary projects.  X
8. Follows technological developments, improves him/herself , easily adapts to new conditions.   X
9. Is aware of ethical, social and environmental impacts of his/her work. X
10. Can present his/her ideas and works in written and oral form effectively; uses English effectively X

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