COURSE UNIT TITLE

: LINEAR SYSTEMS THEORY I

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
EEE 5503 LINEAR SYSTEMS THEORY I ELECTIVE 3 0 0 9

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

ASSOCIATE PROFESSOR SERKAN GÜNEL

Offered to

Industrial Ph.D. Program In Advanced Biomedical Technologies
Industrial Ph.D. Program In Advanced Biomedical Technologies
ELECTRICAL AND ELECTRONICS ENGINEERING (ENGLISH)
Biomedical Tehnologies (English)
ELECTRICAL AND ELECTRONICS ENGINEERING (ENGLISH)
ELECTRICAL AND ELECTRONICS ENGINEERING (ENGLISH)

Course Objective

The course aims to introduce the students concrete bases of the dynamical system theory, and make them familiar with the concepts of Linearization; De nition, solution, stability and qualitative properties of Linear Dynamical Systems; observability and controllability. Realization of linear dynamical canonical systems with also be introduced.

Learning Outcomes of the Course Unit

1   To be familiar with dynamical system concept
2   To be able to use advanced linear algebraic concepts in analysis of dynamical systems
3   To be able to linearize a non-linear dynamical system
4   To be able to use Lyapunov's approach in the analysis of linear dynamical systems.
5   To be able to analyze controlibilty and observability of linear dynamical systems.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Outline & Introduction
2 Mathematical Background (Fields, Vector Spaces, Metrics, Metric Spaces, Norms, Normed Spaces, Inner Products, Inner Product Spaces, Completeness, Banach and Hilbert Spaces)
3 Mathematical Background (Fields, Vector Spaces, Metrics, Metric Spaces, Norms, Normed Spaces, Inner Products, Inner Product Spaces, Completeness, Banach and Hilbert Spaces)
4 Differential Equations (Existence and Uniqueness of solutions, Proof of Fundamental Theorem of Diff. Eq.)
5 System Theory Fundamentals (States and Dynamical Systems, State Transition and Response Functions, Time Invariant and Time varying Systems, Linearization of nonlinear dynamical Systems)
6 Linear Time-Varying Systems (State Transition Matrix and its properties, Solution in terms of state Transition matrix, Impulse Response)
7 Linear Time-Varying Systems (State Transition Matrix and its properties, Solution in terms of state Transition matrix, Impulse Response)
8 Midterm Examination
9 Linear Time Invariant Systems (State Transition Matrix and its Properties, Solution in terms of state Transition matrix, Impulse Response)
10 Stability of Linear D.S (B.I.B.O Stability, Stability in the sense of Liapunov, Kalman Canonical Forms, Minimal Realizations)
11 Stability of Linear D.S (B.I.B.O Stability, Stability in the sense of Liapunov, Kalman Canonical Forms, Minimal Realizations)
12 Stability of Linear D.S (B.I.B.O Stability, Stability in the sense of Liapunov, Kalman Canonical Forms, Minimal Realizations)
13 Observability and Controllability
14 Observability and Controllability

Recomended or Required Reading

1. Chen C, Linear System Theory and Applications, Oxford University Press, 1999
2. Desoer C.A. , A Second Course on Linear Systems Theory, Van Nostrand Reinhold Co, 1970
3. Hespanha J.P , Linear Systems Theory, Princeton University Press, 2009

REFERENCE BOOKS:
1. Kreyszig E, Introduction to Functional Analysis with Applications, John Wiley & Sons, 1978
2. Flemming W. H., Functions of Several Variables, 1964

Planned Learning Activities and Teaching Methods

Lectures with active discussions, weekly homeworks, open book open note examinations

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 ASG ASSIGNMENT
2 MTE MIDTERM EXAM
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE ASG * 0.30 + MTE * 0.30 + FIN * 0.40
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) ASG * 0.30 + MTE * 0.30 + RST * 0.40


Further Notes About Assessment Methods

None

Assessment Criteria

Students' ability to use the learning objectives will be graded using regular homeworks, and midterm examinations.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

To be determined at the begining of the semester

Office Hours

To be determined at the begining of the semester

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 3 39
Preparation for final exam 1 20 20
Preparation for midterm exam 1 15 15
Preparations before/after weekly lectures 12 4 48
Preparing assignments 15 6 90
Midterm 1 4 4
Final 1 4 4
TOTAL WORKLOAD (hours) 220

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10
LO.124533
LO.2432555
LO.323424
LO.43345
LO.535525545

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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