ELE701 - LINEAR SYSTEM THEORY
| Course Name | Code | Semester | Theory (hours/week) |
Application (hours/week) |
Credit | ECTS |
|---|---|---|---|---|---|---|
| LINEAR SYSTEM THEORY | ELE701 | Any Semester/Year | 3 | 0 | 3 | 10 |
| Prequisites | None | |||||
| Course language | Turkish | |||||
| Course type | Elective | |||||
| Mode of Delivery | Face-to-Face | |||||
| Learning and teaching strategies | Lecture Question and Answer Problem Solving | |||||
| Instructor (s) | Department Faculty | |||||
| Course objective | Many 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 |
| |||||
| Course Content | Linear 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. | |||||
| References | 1. 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
| Weeks | Topics |
|---|---|
| Week 1 | Linear spaces : field, linear space, subspace, span, linear independence, dimension, basis, change of basis. |
| Week 2 | Linear oprerators and representations of a linear operator. |
| Week 3 | Linear operators: range and null spaces, eigenvalues and eigenvectors, Jordan form representation. |
| Week 4 | Polynomial of a square matrix, minimal polynomial, function of a square matrix, norms and inner product. |
| Week 5 | Linear system description: input-output approach (for both time-invariant and time varying). |
| Week 6 | Linear system description: state variable approach (for both time-invariant and time varying). |
| Week 7 | Solution of dynamical equations, fundamental martix and state transition matrix. |
| Week 8 | Solution of dynamical equation, computation of eAt and (SI-A)-1, Faddeev algorithm, modal decomposition. |
| Week 9 | Equivalent (or similar) systems and equivalence (or similarity) transformation. |
| Week 10 | Midterm 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 15 | Final exam |
| Week 16 | Final exam |
Assesment methods
| Course activities | Number | Percentage |
|---|---|---|
| Attendance | 0 | 0 |
| Laboratory | 0 | 0 |
| Application | 0 | 0 |
| Field activities | 0 | 0 |
| Specific practical training | 0 | 0 |
| Assignments | 6 | 10 |
| Presentation | 0 | 0 |
| Project | 0 | 0 |
| Seminar | 0 | 0 |
| Midterms | 1 | 40 |
| Final exam | 1 | 50 |
| Total | 100 | |
| Percentage of semester activities contributing grade succes | 0 | 50 |
| Percentage of final exam contributing grade succes | 0 | 50 |
| Total | 100 | |
WORKLOAD AND ECTS CALCULATION
| Activities | Number | Duration (hour) | Total Work Load |
|---|---|---|---|
| Course Duration (x14) | 13 | 3 | 39 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Specific practical training | 0 | 0 | 0 |
| Field activities | 0 | 0 | 0 |
| Study Hours Out of Class (Preliminary work, reinforcement, ect) | 14 | 9 | 126 |
| Presentation / Seminar Preparation | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework assignment | 6 | 6 | 36 |
| Midterms (Study duration) | 1 | 25 | 25 |
| Final Exam (Study duration) | 1 | 30 | 30 |
| Total Workload | 35 | 73 | 256 |
Matrix Of The Course Learning Outcomes Versus Program Outcomes
| D.9. Key Learning Outcomes | Contrubition level* | ||||
|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |
| 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