TYPE OF COURSE UNIT	Compulsory Course
LEVEL OF COURSE UNIT	Master's Degree With Thesis
YEAR OF STUDY	-
SEMESTER	-
NUMBER OF ECTS CREDITS ALLOCATED	10
NAME OF LECTURER(S)	Professor Sedat Nazlıbilek
LEARNING OUTCOMES OF THE COURSE UNIT	At the end of this course, the students; 1) Learn and apply linear algebra. 2) Will be able to model linear systems. 3) Learn controllability and observability concepts. 4) Will be able to carry out analysis of linear systems. 5) Gain problem solving skills for linear system problems. 6) Will be able to utilize the related software for linear systems.
MODE OF DELIVERY	Face to face
PRE-REQUISITES OF THE COURSE	No
RECOMMENDED OPTIONAL PROGRAMME COMPONENT	None
COURSE DEFINITION	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 1st Week Linear space, basis vectors 2nd Week Grammina matrix, linear operators, similarity transformation 3rd Week Range and null spaces, norms 4th Week Gram-Schmidt orthonormalization, SVD 5th Week Eigenvectors, Jordan form 6th Week Midterm Exam 1 7th Week Function of a square matrix, Minimal polynomial 8th Week Linear system decriptions, discrete-time systems 9th Week State transition matrix, solutions of state equations 10th Week Modal decomposition, Linear time-varying systems 11th Week Midterm Exam 2 12th Week Controllability/observability, Kalman decomposition 13th Week Stability, BIBO stability, Lyapunov stability analysis 14th Week Stability of discrete-time systems
RECOMENDED 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 WORKLOAD	Activities Number Hours Workload 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 Workload 300 Total Workload / 30 10 ECTS Credits of the Course 10
LANGUAGE OF INSTRUCTION	Turkish
WORK PLACEMENT(S)	No