COURSE UNIT TITLE

: LINEAR SYSTEMS THEORY II

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
EEE 5502 LINEAR SYSTEMS THEORY II 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 NON -THESIS (EVENING PROGRAM) (ENGLISH)
ELECTRICAL AND ELECTRONICS ENGINEERING (ENGLISH)
ELECTRICAL AND ELECTRONICS ENGINEERING (ENGLISH)

Course Objective

Main objective of the course is to introduce advanced level system theory concepts beyond stability and to set the stage for more advanced topics. The controllablity and obserablility concepts will be discussed in detail. a special emphasis will be on realizations of linear time invariant systems in controllable and canonical forms. The minimality of realizations of Multi Input Multi Output systems is to be disscused. Linear state and output feedback methods in MIMO systems will be disscussed in detail. The concept of Linear Quadratic Regulation will be introduced.

Learning Outcomes of the Course Unit

1   To be able to calculate controbility and observability Grammians and solutions of Lyapunov Equations
2   To be able to design minimal linear time invariant systems
3   To be able to design balanced minimal linear time invarianf systems
4   To be able to design multi input multi output linear feedback systems
5   To be able to desing full and reduced state estimators, and design feedback systems using them
6   To be able to design output feedback linear systems

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Introduction and Review of Linear System Theory Concepts Review of Solution of Linear Time Variant and Invariant Systems Review of Stability Concepts
2 Controllability in Detail Definition of Reachability and Controllability, Reachability and Controllability Grammians Controllability Matrix for LTI systems Controllability Tests Controllable Decompositions State Feedback and Stabilizability
3 Controllability 2
4 Observability in Detail Definition of Observability and Constructibility Observability and Constructibility Gramians Duality Observability Tests Kalman Decomposition Theorem Definition of Detectability Detectability Tests State Estimation Stabilization through output Feedback The students must choose the subject of their term project
5 Observability 2
6 Midterm Examination
7 Minimal Realizations Similarity of Minimal Realizations
8 Minimal Realization 2
9 Minimal Realizations 3
10 Poles and Zeros of MIMO systems Smith-McMillan Form McMillan Degree, Poles ans Zeros, Order of minimal realizations System Inverse and its poles and zeros
11 Linear Quadratic Regulation (LQR) Optimal Regulation Problem Feedback Invariants Optimal State Feedback Frequency Domain and Asymptotic properties of LQR
12 Output Feedback Certainty Equivalence Minimum Energy Estimation Stochastic Linear Quadratic Gaussian Estimation LQG LQR/LGR output Feedback
13 Output Feedback 2

Recomended or Required Reading


ITEXTBOOK :
Chen, C.T., Linear system Theory And Design, Oxford University Press, 1984
Hespanha, J.P., Linear Systems Theory, Princeton University Press, 2009

REFERENCE BOOKS :
Zadeh A.L, Desoer C.A., Linear System Theory- The State Space Approach, Dover Publications, 1991

Planned Learning Activities and Teaching Methods

Lectures with active discussions, regular homeworks almost every week, a midterm and a final examination. Students must also apply the concepts on a term projects.

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

The ability to use the concept in learning objectives will be measured with weekly homework assignments, a term project , one openbook open midterm and final 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
Design Project 1 30 30
Preparations before/after weekly lectures 12 3 36
Preparation for midterm exam 1 15 15
Preparation for final exam 1 15 15
Preparing assignments 15 4 60
Midterm 1 4 4
Final 1 4 4
TOTAL WORKLOAD (hours) 203

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13PO.14PO.15
LO.153333
LO.253333
LO.353333
LO.453333
LO.553333
LO.6

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