Title  ΜΟΝΤΕΡΝΑ ΘΕΩΡΙΑ ΕΛΕΓΧΟΥ / Modern Control Theory 
Code  0462 
Faculty  Sciences 
School  Mathematics 
Cycle / Level  1st / Undergraduate 
Teaching Period  Spring 
Coordinator  Nikolaos Karampetakis 
Common  No 
Status  Active 
Course ID  40000486 
Programme of Study: UPS of School of Mathematics (2014today)
Registered students: 241
Orientation  Attendance Type  Semester  Year  ECTS 

Core  Elective Courses  Spring    5 
Academic Year  2019 – 2020 
Class Period  Spring 
Faculty Instructors 

Weekly Hours  3 
Class ID  600147697

Type of the Course
 Scientific Area
 Skills Development
Course Category
Knowledge Deepening / Consolidation
Mode of Delivery
 Face to face
Digital Course Content
 eStudy Guide https://qa.auth.gr/en/class/1/600147697
 eLearning: http://anemos.web.auth.gr/
 Other: http://eclass.auth.gr/courses/MATH100/
Language of Instruction
 Greek (Instruction, Examination)
Learning Outcomes
Upon the successful completion of this course a student will be able to:
a) transform the description of a linear, timeinvariant, multivariable system to all possible descriptions (transfer function matrix, state space description etc.
b) calculate and plot the time response of a state space system,
c) transform of a given state space system to various canonical forms,
d) design the block diagram and signal flow of a system described by state space equations,
e) check system properties such as controllability , stabilizability, observability, and detectability,
f) calculate and design a compensator capable to place the poles of the system to a specific region,
g) calculate and design an optimal controller,
h) calculate and design a system observer,
i) create a controller that will use an oberver for the estimation of the states,
j) to apply the separation principle.
General Competences
 Apply knowledge in practice
 Retrieve, analyse and synthesise data and information, with the use of necessary technologies
 Adapt to new situations
 Make decisions
 Work in teams
Course Content (Syllabus)
State space models of LTI continuous time systems. Single input – single output systems. Multivariable systems. Block diagrams and realizations of state space models. Examples. System equivalence and state space coordinate transformations. Examples. Eigenvalues and eigenvectors. Diagolalization of matrices and diagonalization of state space models by coordinate transformations. State space realizations of transfer functions. State space system responses. Unit impulse and unit step response of state space models. LTI systems. Free and forced response of state space models. Canonical forms of state space models. Controllability. Observaability. Controllability and Obserability criteria. Stabilization of state space models and decoupling zeros. Stability of state space models. Eigenvalue criteria for stability. Asymptotic and BIO stability. State feedback. Eigenvalue assignment by state feedback. Constant output feedback. State Observers and state reconstruction. Stabilization by state observers and state feedback. The separation principle.
Keywords
state space systems, modern control theory, controllability, observability, pole placement, observers, stability
Educational Material Types
 Notes
 Slide presentations
 Book
Use of Information and Communication Technologies
Use of ICT
 Use of ICT in Course Teaching
 Use of ICT in Laboratory Teaching
 Use of ICT in Communication with Students
Course Organization
Activities  Workload  ECTS  Individual  Teamwork  Erasmus 

Lectures  39  1.3  
Laboratory Work  13  0.4  
Reading Assigment  98  3.3  
Exams  
Total  150  5 
Student Assessment
Description
 Written exams at the end of the semester.
 Optional monitoring a laboratory course where the result of the examination will count 30% of the final score. The remaining 70% of the score will come from the final exams.
Student Assessment methods
 Written Assignment (Summative)
 Written Exam with Problem Solving (Formative, Summative)
 Labortatory Assignment (Formative)
Bibliography
Course Bibliography (Eudoxus)
 Εισαγωγή στην Μαθηματική Θεωρία Σημάτων, Συστημάτων και Ελέγχου, Τόμος Β. Μοντέρνα Θεωρία Ελέγχου του Α. Βαρδουλάκη.
 Γραμμικά συστήματα αυτομάτου ελέγχου των E. Charles, G. Donald, L. James, J. Melsa, C. Rohrs, D. Schultz.
 Linear Systems [electronic resource] των P. J. Antsaklis, A. N. Michel.
Additional bibliography for study
1. Antsaklis P. and Michel A.N., 1977, Linear Systems, The McGrawHill Companies Inc. New York.
2. Chen C.T., 1970, Introduction to Linear System Theory, Holt, Renehart and Winston Inc. New York.
3. Kailath T., 1980, Linear Systems, Prentice Hall.
4. Wolovich W.A., 1974, Linear Multivariable Systems, Springer Verlag, New York.
Last Update
15032020