Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course To study the fundemental concepts of mathematical control theory
Course Content State Space Fundamentals, Reachability and Controllability, Detectability and Observability, Minimal Realizations, BIBO and Asymptotic stability, Design of Linear State Feedback Control Laws, Observers and Dynamic Feedback
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator Instructor Dr. Gökhan Şahan
Name of Lecturers Associate Prof.Dr. Enver Tatlıcıoğlu
Instructor Dr. Gökhan Şahan
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Mathematical Control Theory, E.Sontag, Springer , 1998
Linear state space control systems, Robert Williams, Douglas Lawrance, Wiley Press, 2007
Mathematical Control Theory, Jery Zabczyk, Birkhauser, 1992

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 50
Quizzes 0 % 0
Homeworks 2 % 10
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 40
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 1 36 36
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 2 25 50
Application (Homework, Reading, Self Study etc.) 2 15 30
Exams and Exam Preparations 2 30 60
Total Work Load   Number of ECTS Credits 6 176

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 To identify the fundemental concepts in State Space
2 To understand the reachability and controllability of a system
3 To understand the detectability and observability of systems
4 to understand the transformation between state space and transfer function representations
5 to identify the linear feedback methods of the systems
6 to identify the observers and observer design methods
7 to identify the stability and stabilization of systems

Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 State Equation Solution, Impulse Response
2 Laplace Domain representations, State Space realizations
3 Fundemental results on reachability and controllability
4 Coordinate transformations, Canonical forms ve Controllability tests
5 Fundemental results on detectability and observability
6 Observable canonical forms and coordinate transformations
7 Tests for observability
8 MIMO and SISO Realizations
9 Stability, internal stability
10 BIBO stability
12 BIBO stabiliyy versus symptotic stability
13 Linear State feedback and stabilization
14 Observers and Observer design

Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 2 2 3 3 3
C2 2 2 3 3 3
C3 2 2 3 3 3
C4 2 2 3 3
C5 2 2 3 3
C6 2 2 3 3
C7 2 2 3 3 3

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant