GRADUATE SCHOOL
Ph.D. In Electrical-Electronics Engineering
EEE 551 | Course Introduction and Application Information
| Course Name |
Linear Systems Theory
|
|
Code
|
Semester
|
Theory
(hour/week) |
Application/Lab
(hour/week) |
Local Credits
|
ECTS
|
|
EEE 551
|
Fall/Spring
|
3
|
0
|
3
|
7.5
|
| Prerequisites |
None
|
|||||
| Course Language |
English
|
|||||
| Course Type |
Elective
|
|||||
| Course Level |
Second Cycle
|
|||||
| Mode of Delivery | - | |||||
| Teaching Methods and Techniques of the Course | - | |||||
| Course Coordinator | ||||||
| Course Lecturer(s) | ||||||
| Assistant(s) | - | |||||
| Course Objectives | The course aims the students: i) to get a solid mathematical background on real analysis, normed linear spaces and linear differential equations in the state form. ii) to gain basic skills in analyzing a given linear time-invariant dynamical system; determining whether or not the system has a well-defined solution, so analyzing qualitative properties of solutions, and analyzing the stability, controllability and observability of linear dynamical systems, and iii) to have a dynamical system view. |
| Learning Outcomes |
The students who succeeded in this course;
|
| Course Description | Real analysis. Algebraic structures. Linear spaces and transformations. State equations. Existence and uniqueness of solutions. Properties of dynamical systems. State transition matrix for linear time-invariant systems. Zero-state solutions. Zero-input solutions. Minimal polynomial and Cayley-Hamilton theorem. Eigenvalues and eigenvectors. Jordan form. Stability in the sense of Liapunov.Bounded-Input Bounded-Output Stability. Controllablity and observability. Minimal realization. |
|
|
Core Courses |
X
|
| Major Area Courses | ||
| Supportive Courses | ||
| Media and Management Skills Courses | ||
| Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
| Week | Subjects | Related Preparation |
| 1 | Set theory overview. Ordering relation. Greatest and least elements | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 2 | Algebraic structures: Group, ring, field and linear space. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 3 | Normed, metric and inner-product spaces. Vector and matrix norms. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 4 | Derivation of state equations from systems. Existence and uniqueness of solutions. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 5 | Fundamental matrix and state transition matrix of linear state equations. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 6 | Zero-input, zero-state and complete solutions. Impulse response matrix. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 7 | Benzerlik dönüşümü ile köşegenleştirme. Rezidü matrisleri. Karakteristik ve minimal polinaomlar. Cayley-Hamilton Teoremi. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 8 | Generalized eigenvalues and Jordan form for state matrix. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 9 | 1. Midterm | |
| 10 | Liapunov stability of linear time-invariant and time-varying systems. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 11 | Liapunov stability of linear time-invariant and time-varying systems. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 12 | Controllability of linear time-invariant and time-varying systems. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 13 | 2. Midterm | |
| 14 | Controllability of linear time-invariant and time-varying systems. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 15 | Minimal realization of linear time-invariant dynamical systems. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 16 | Review of the Semester |
| Course Notes/Textbooks | The textbook referenced above and lecture notes |
| Suggested Readings/Materials | Related Books |
EVALUATION SYSTEM
| Semester Activities | Number | Weigthing |
| Participation |
1
|
10
|
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | ||
| Portfolio | ||
| Homework / Assignments | ||
| Presentation / Jury | ||
| Project | ||
| Seminar / Workshop | ||
| Oral Exams | ||
| Midterm |
2
|
40
|
| Final Exam |
1
|
50
|
| Total |
| Weighting of Semester Activities on the Final Grade |
3
|
50
|
| Weighting of End-of-Semester Activities on the Final Grade |
1
|
50
|
| Total |
ECTS / WORKLOAD TABLE
| Semester Activities | Number | Duration (Hours) | Workload |
|---|---|---|---|
| Theoretical Course Hours (Including exam week: 16 x total hours) |
16
|
3
|
48
|
| Laboratory / Application Hours (Including exam week: '.16.' x total hours) |
16
|
0
|
|
| Study Hours Out of Class |
15
|
4
|
60
|
| Field Work |
0
|
||
| Quizzes / Studio Critiques |
0
|
||
| Portfolio |
0
|
||
| Homework / Assignments |
10
|
0
|
|
| Presentation / Jury |
5
|
0
|
|
| Project |
0
|
||
| Seminar / Workshop |
0
|
||
| Oral Exam |
0
|
||
| Midterms |
2
|
40
|
80
|
| Final Exam |
1
|
37
|
37
|
| Total |
225
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
|
#
|
Program Competencies/Outcomes |
* Contribution Level
|
||||
|
1
|
2
|
3
|
4
|
5
|
||
| 1 | Accesses information in breadth and depth by conducting scientific research in Electrical and Electronics Engineering; evaluates, interprets and applies information. | X | ||||
| 2 | Is well-informed about contemporary techniques and methods used in Electrical and Electronics Engineering and their limitations. | X | ||||
| 3 | Uses scientific methods to complete and apply information from uncertain, limited or incomplete data; can combine and use information from different disciplines. Knows and applies the research methods in studies of the area with a high level of skill. |
X | ||||
| 4 | Is informed about new and upcoming applications in the field and learns them whenever necessary. | X | ||||
| 5 | Defines and formulates problems related to Electrical and Electronics Engineering, develops methods to solve them and uses progressive methods in solutions. Can independently realize novel studies that bring innovation to the field, or methods, or design, or known methods. |
X | ||||
| 6 | Develops novel and/or original methods, designs complex systems or processes and develops progressive/alternative solutions in designs. | X | ||||
| 7 | Designs and implements studies based on theory, experiments and modeling; analyses and resolves the complex problems that arise in this process. Performs critical analysis, synthesis and evaluation of new and complex ideas. | X | ||||
| 8 | Can work effectively in interdisciplinary teams as well as teams of the same discipline, can lead such teams and can develop approaches for resolving complex situations; can work independently and takes responsibility. | X | ||||
| 9 | Engages in written and oral communication at least in Level C1 of the European Language Portfolio Global Scale. | X | ||||
| 10 | Communicates the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form. |
X | ||||
| 11 | Evaluates the results of scientific, technological and engineering research and development activities in terms of the social, environmental, health, safety and legal aspects. Examines social relations and norms related to the field, and develops and makes attempts to change them if necessary. Knows their project management and business applications, and is aware of their limitations in Electrical and Electronics Engineering applications. |
X | ||||
| 12 | Highly regards scientific and ethical values in data collection, interpretation, communication and in every professional activity. Adheres to the principles of research and publication ethics. |
X | ||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest