LINEAR SYSTEM THEORY II

EEM614

Course Code: EEM614
Semester: -
Theory+Practice: 3 + 0
ECTS: 10

Course Type

Elective Course

Course Level

Doctorate Of Science

Year of Study

Semester

ECTS

Name of Lecturer(s)

Learning Outcomes

At the end of this course, the students;

Learn and apply linear algebra.
Will be able to model linear systems.
Learn controllability and observability concepts.
Will be able to carry out analysis of linear systems.
Gain an ability to solve problems for linear system.
Will be able to utilize the related software for linear systems.

Mode of Delivery

Face to face

Prerequisites

Recommended Optional Programme Components

None

Course Description

Review of transformations. Linear vector spaces. Linear operators. Eigenvector analysis, Jordan form. Singular Value Decomposition. Linear systems; input-output and state variables, time-invariant and time varying systems. Discrete-time systems. Analysis of linear systems; controllability, observability, Kalman decomposition, BIBO stability, asymptotic stability, Lyapunov stability criteria. Stability of discrete-time systems.

Course Contents

WEEK	TOPICS
1^st Week	Linear space, basis vectors
2^nd Week	Grammina matrix, linear operators, similarity transformation
3^rd Week	Range and null spaces, norms
4^th Week	Gram-Schmidt orthonormalization, SVD
5^th Week	Eigenvectors, Jordan form
6^th Week	Midterm Exam 1
7^th Week	Function of a square matrix, Minimal polynomial
8^th Week	Linear system decriptions, discrete-time systems
9^th Week	State transition matrix, solutions of state equations
10^th Week	Modal decomposition, Linear time-varying systems
11^th Week	Midterm Exam 2
12^th Week	Controllability/observability, Kalman decomposition
13^th Week	Stability, BIBO stability, Lyapunov stability analysis
14^th Week	Stability of discrete-time systems

Recommended or Required Reading

1. Uraz, A., "Linear System Theory", Lecture Notes, 2003
2. Chen, C.T. "Linear System Theory and Design", Third Ed., Oxford, 1998

Planned Learning Activities and Teaching Methods

Lecture
Questions/Answers

Assessment Methods and Criteria

	Quantity	Percentage (%)
Mid-term	2	50
Assignment	1	5
Attendance	1	5
Total(%)		60
Contribution of In-term Studies to Overall Grade(%)		60
Contribution of Final Examination to Overall Grade(%)		40
Total(%)		100

ECTS Allocated Based on Student Workload

Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Midterm exam	1	3	3
Preparation for Quiz	0	0	0
Individual or group work	14	8	112
Preparation for Final exam	1	40	40
Course hours	14	3	42
Preparation for Midterm exam	1	30	30
Laboratory (including preparation)	0	0	0
Final exam	1	3	3
Homework	2	35	70
Total Work Load			300
Total Work Load / 30 (h)			10
ECTS Credit of the Course			10

Language of Instruction

Turkish

Work Placement(s)

Programme Qualifications / Learning Outcomes

	LO1	LO2	LO3	LO4	LO5	LO6
K1					X
K2
K3	X	X	X	X	X
K4			X	X
K5						X
K6
K7
K8
K9
K10
K11