Master TR-NQF-HE: Level 7 QF-EHEA: Second Cycle EQF-LLL: Level 7

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MCH5001 Linear System Theory Spring 3 0 3 6
The course opens with the approval of the Department at the beginning of each semester

Basic information

Language of instruction: En
Type of course: Departmental Elective
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Dr. Öğr. Üyesi MUSTAFA EREN YILDIRIM
Course Objectives: To provide advanced system theoretic concepts with emphasis on linear systems.

Learning Outputs

The students who have succeeded in this course;
Students will be able
- to define a dynamical system as a mathematical object
- to comprehend linearity and time-invariance
- to relate time- and frequency-domain representations of linear time-invariant (LTI) systems
- to determine response of LTI systems to specific inputs
- to understand the concept of controllability and to relate it to such problems as setting up the initial conditions, eigenvalue placement by state feedback, stabilization by optimal feedback control
- to understand the concept of observability and to relate it to such problems as calculation of the initial conditions and observer design

Course Content

Dynamical system representation. State-space representation of continuous-time (CT) systems: Solution of CT state equations, impulse response, convolution integral. State-space representation of discrete-time (DT) systems: solution of DT state equations, pulse response, convolution sum. Modes of unforced solutions. Transfer function. Controllability and state feedback. Observability and observer design. Dynamic output feedback

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Dynamical system representation. Concept of state. Causality.
2) Finite state, finite dimensional and infinite dimensional systems. Lineariy and time-invariance.
3) State space representation of continuous-time (CT) linear systems. State transition matrix.
4) State-space representation of CT linear, time-invariant (LTI) systems. Impulse response and transfer function matrices.
5) Modes of CT LTI systems. Modal decomposition of solutions.
6) Discrete-time (DT) LTI systems.
7) Sampled-data systems.
8) Review and midterm exam
9) Controllability of LTI systems. Setting up the initial conditions.
10) Observability of LTI systems. Calculation of the initial state.
11) Canonical decomposition. Separation of controllable and unobservable subspaces.
12) Eigenvalue assignment by state-feedback.
13) Observer design.
14) Pole placement by dynamic output feedback.


Course Notes: - W.L. Brogan, Modern Control Theory, Prentice Hall
References: - C-T. Chen, Linear System Theory and Design, HRW

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Attendance % 0
Laboratory % 0
Application % 0
Field Work % 0
Special Course Internship (Work Placement) % 0
Quizzes % 0
Homework Assignments 5 % 25
Presentation % 0
Project % 0
Seminar % 0
Midterms 1 % 25
Preliminary Jury % 0
Final 1 % 50
Paper Submission % 0
Jury % 0
Bütünleme % 0
Total % 100
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Laboratory 0 0 0
Application 0 0 0
Special Course Internship (Work Placement) 0 0 0
Field Work 0 0 0
Study Hours Out of Class 15 9 135
Presentations / Seminar 0 0 0
Project 0 0 0
Homework Assignments 5 5 25
Quizzes 0 0 0
Preliminary Jury 0
Midterms 1 3 3
Paper Submission 0
Jury 0
Final 1 3 3
Total Workload 208

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
Program Outcomes Level of Contribution
1) Gains an academic background and abilities for making scientific research; analysis, interpretation and application of knowledge in subjects of Mechatronics Engineering.
2) Acquires an ability to select, apply and develop modern techniques and methods for mechatronics engineering applications.
3) Develops new and innovative ideas, procedures and solutions in the design of mechatronics systems, components and processes.
4) Gains an ability for experimental design, data accumulation, data analysis, reporting and implementation.
5) Acquires abilities for individual and team-work, communication and collaboration with team members and interdisciplinary cooperation.
6) Gains an ability to communicate effectively oral and written; and a knowledge of English sufficient to follow technical developments and terminology.
7) Acquires recognition of the need for, and an ability to access and report knowledge, to engage in life-long learning.
8) Gains an understanding of universal, social and professional ethics.
9) Acquires a knowledge of business-oriented project organization and management; awareness of entrepreneurship, innovation and sustainable development
10) Gains awareness for the impact of mechatronics engineering applications on human health, environmental, security and legal issues in a global and social context.