COURSE UNIT TITLE

: NONLINEAR SYSTEMS THEORY

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
EEE 5102 NONLINEAR SYSTEMS THEORY ELECTIVE 3 0 0 8

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

ELECTRICAL AND ELECTRONICS ENGINEERING (ENGLISH)
ELECTRICAL AND ELECTRONICS ENGINEERING (ENGLISH)
ELECTRICAL AND ELECTRONICS ENGINEERING (ENGLISH)

Course Objective

The objective of the course is to indroduce main concepts and analysis methods of nonlinear systems theory by a functional analysis point of view. Following topics will be covered though out the course: Contraction mapping theorem, Analytical methods for second and higher order dynamical systems, Lyapunovs direct and indirect methods for the stability of nonlinear nonautonomous dynamical systems, Lures problem, Absolute stability, Input-output stability of nonlinear feedback systems in Lp spaces, Reachability, observability, linearization and stabilization of nonlinear control systems.

Learning Outcomes of the Course Unit

1   To be able to qualitatively analyze nonlinear systems
2   To be able to assess stability properties of nonlinear systems
3   To be able to use bifurcation analysis in analysis of dynamical systems
4   To be able to use Lyapunov's direct and indirect methods to study stability of solutions of nonlinear systems
5   To be able to analyze controlability of nonlinear 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 (Review of the theory of the ordinary differential equations, dynamical systems, qualitative integration of dynamical systems)
3 Mathematical Background 2
4 Mathematical Background 3
5 Planar Dynamical Systems
6 Planar dynamical systems 2
7 Input-Output Analysis
8 Input Output Analysis 2
9 Midterm Examination
10 Lyapunov Stability Theory and its Applications in Nonlinear System
11 Lyapunovs direct and indirect methods
12 Lyapunovs direct and direct methods 2
13 Bifurcation Theory
14 Bifurcation Theory 2

Recomended or Required Reading

Textbook(s):
Sastry S.,"Nonlinear Systems; Analysis, Stability, and Control", Springer Verlag, 1999.
Supplementary Books:
Shilnikov L.P., Shilnikov A.L. Turaev D.V. And Chua L. O. Methods of Qualitative Theory In Nonlinear Dynamics Part I , World Scientific, 1998
Kreyszig E, Introduction to Functional Analysis with Applications, John Wiley & Sons, 1978
Flemming W. H., Functions of Several Variables, 1964

Planned Learning Activities and Teaching Methods

Lecture+Homeworks+Project +Exam

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


*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

Homeworks, Formal examinations,

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

To be announced.

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 3 42
Preparations before/after weekly lectures 10 4 40
Preparation for final exam 1 25 25
Preparation for midterm exam 1 25 25
Preparing assignments 10 5 50
Final 1 4 4
Midterm 1 4 4
TOTAL WORKLOAD (hours) 190

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13PO.14
LO.1521322
LO.2521322
LO.3521322
LO.4521322
LO.5

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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