KOM 501E – Control of Systems with Parameter Uncertainties

About the Course

Course Code: KOM 501E
Term: 2025 Fall
Lecturer: Prof. Dr. M. Turan Söylemez
Control and Automation Eng. Dept.
Room Num: 4207, Tel: 212 - 285 35 70
Course Place - Hours: D5101 - Monday (09:30 - 12:29)
Course Books: 1) "Robust Control: Systems with Uncertain Physical Parameters", J Ackermann, 1993, Springer-Verlag.
"Robust Control: The Parameter Space Approach", 2nd ed, J Ackermann, 2002, Springer-Verlag, ISBN:1-85233-514-9.
2) "New Tools for Robustness of Linear Systems", B R Barmish, 1994, Macmillan
3) "Robust Control: The Parametric Approach", S P Bhattacharyya, H Chapellat and L H Keel, 1995, Prentice-Hall
4) "Linear Control Theory: Structure, Robustness and Optimization", 2009, S. P. Bhattacharyya, A Datta, L H Keel, CRC Press, ISBN: 978-0-8493-4063-5
5) "Pole Assignment for Uncertain Systems", M. T. Söylemez, 1999, RSP Press
6) "Robust Control of Uncertain Dynamic Systems", R K Yedavalli, 2014, Springer
7) "Systems with Parametric Uncertainty: An Algebraic Approach to Robust Control Design", Radek Matusu, 2010, Lambert Academic Publishing
Grading Policy: 24% Midterm Exam
21% Homework
20% Final Project
35% Final Exam
Final Exam Enterance Condition: Weighted average of the first two Homework Assignments and the midterm exam must be at least 25.
Home Page: http://web.itu.edu.tr/soylemezm/kom501e

Course Syllabus

Date Topics to be covered
September 29
(Week 1)		 NO CLASS DUE TO ITU OPENING CEREMONY
October 6
(Week 2)		 INTRODUCTION

  • Motivation
  • Definition of Robust Control
  • Classification of Robust Control Systems
  • Introduction to parametric uncertain systems
    		•
    October 13
    (Week 3)    		 MODELING OF PARAMETRIC UNCERTAIN SYSTEMS

  • Examples for modeling systems with parameter uncertainty
  • Introduction to the notation and general concepts
  • Symbolic algebra and parametric uncertain systems
  • Generalization of several control concepts to parametric uncertain systems
    • Stability
    • Controllability & Observability
    		•
    October 20
    (Week 4)    		 ROBUST STABILITY ANALYSIS

  • Pole Spread and gridding
  • Boundary crossing theorem
  • Algebraic tests
  • Routh table
    MATHEMATICA TUTORIAL
    		•
    October 27
    (Week 5)    		 ROBUST STABILITY ANALYSIS

  • Hurwitz determinants
  • Bialas theorem
    		•
    November 3
    (Week 6)    		 FREQUENCY RESPONSE of POLYNOMIALS with PARAMETRIC UNCERTAINTIES

  • Mikhailov Theorem
  • Hermite-Biehler Theorem
  • Value Set Concept
  • Zero Exclusion Theorem
  • Singular Frequency
    		•
    November 10
    (Week 7)    		 CLASSIFICATION OF PARAMETRIC UNCERTAIN POLYNOMIALS and TEST SETS

  • Classification
  • Interval polynomials
  • Affine-linear polynomials
  • Multilinear polynomials
  • Polynomials with polynomial coefficients
  • Test Sets
  • Kharitonov theorem
    		•
    November 17
    (Week 8)    		 TEST SETS (CONT.)

  • The concept of conservatism
  • Edge theorem
    		•
    November 24
    (Week 9)    		 MIDTERM EXAM
    December 1
    (Week 10)    		 TEST SETS (CONT.)

  • Test sets for multilinear polynomials
  • Jacobi conditions for uncertain parameters
  • Mapping Theorem
  • Test sets for polynomials with polynomial uncertainties.
    		•
    December 8
    (Week 11)    		 CONSTRUCTION OF VALUE SETS

  • Addition and multiplication of value sets
  • Tree structured decomposition
    		•
    December 15
    (Week 12)    		 STABILITY RADIUS

  • Tsypkin - Polyak Loci
  • Interval polynomials
  • Affine linear polynomials
  • Largest hypersphere in the parameter space
    		•
    December 22
    (Week 13)    		 ROBUSTNESS ANALYSIS of FEEDBACK SYSTEMS

  • Box Theorem
  • Positive interval plants
  • Robustness with respect to nonlinearities
    		•
    December 29
    (Week 14)    		 STABILIZING PID CONTROLLER DESIGN

  • Stabilizing P Controllers
  • Stabilizing PI Controllers
  • Stabilizing PID Controllers
    		•
    January 5
    (Week 15)    		 FINAL PROJECT PRESENTATIONS