MCH5001 Linear System TheoryBahçeşehir UniversityDegree Programs MECHATRONICS ENGINEERING (ENGLISH, NONTHESIS)General Information For StudentsDiploma SupplementErasmus Policy StatementNational Qualifications
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 Fall 3 0 3 8

Basic information

Language of instruction: English
Type of course: Must Course
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Dr. Öğr. Üyesi MUSTAFA EREN YILDIRIM
Recommended Optional Program Components: None
Course Objectives: To provide advanced system theoretic concepts with emphasis on linear systems.

Learning Outcomes

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 / Textbooks: - 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
Homework Assignments 5 % 25
Midterms 1 % 25
Final 1 % 50
Total % 100
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Study Hours Out of Class 15 9 135
Homework Assignments 5 5 25
Midterms 1 3 3
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