Spring 2022 Edition of ECE 675 Homepage

Introduction to Analysis of Non-linear Systems


·          January 28, 2022   A paper related to FunWork #1 posted---see below. Its title is “A model of intelligent controller of hypothyroidism treatment.”

·          January 19, 2022   Alternative FunWork #1 posted dealing with modeling different types of networks using a Brain-State-in-a-Box neural network

·          January 11, 2022   Welcome to ECE 675


Stan Żak

School of Electrical and Computer Engineering

Purdue University

465 Northwestern Avenue
West Lafayette, IN 47907-2035
Ph: (765) 494-6443
e-mail: zak@purdue.edu

Class Hours

T,Th: 9:00--10:15am in EE 226

Office Hours

M,W,F: 12:30--1:30pm


Elements of linear algebra, ordinary differential equations, calculus of several variables. In particular: matrix manipulation, linear spaces, quadratic forms, differentiation of real-valued functions of n variables, gradients, the chain rule. Working knowledge of linear dynamic systems.


S. H. Żak, Systems and Control, Oxford University Press, New York, 2003

Computer Software

MATLAB (a math-tools program)

Course Objective

 “Real world” control problems are non-linear. Design techniques based on the linear system theory have difficulties with accommodating non-linear effects and modeling uncertainties. In this course, we study different approaches to the analysis and design of non-linear and uncertain, dynamical control systems. We then apply these methods to modeling and analysis of biological systems, specifically two endocrine systems are analyzed in order to demonstrate the power of non-linear methods.

Upon completion of the course, the student should understand common non-linear phenomena. The student will become familiar with concepts and tools that are useful in the analysis of non-linear systems and in the design of controllers and observers for such systems. The emphasis will be on design to show how nonlinear system theory fits into practical applications.

Brief Course Description

An introduction to modeling of dynamical control systems. State-plane and numerical methods for solving modeling equations. Linearization techniques. Stability. Controller and observer design for non-linear systems. Variable structure sliding-mode control. Vector field techniques. Introduction to chaos. Decentralized control of non-linear large-scale systems.

Course Outline







·         LaSalle’s invariance principle

o    Video

o    Two interesting examples illustrating LaSalle’s invariance principle

o    A generalization of the LaSalle’s principle and its application to the information systems


·         Observer design for systems with unknown inputs


·         Linear Matrix Inequalities








·         Potential extra topic





·         The assignments must be typed. Recommended package for typing math is LaTeX. A friendly introduction to LaTeX is the book by Jane Hahn, LaTEX for Everyone.

·         Clearly identify the steps you have taken to solve each problem.

·         Your grade depends on the completeness and clarity of your work as well as the resulting answer.

·         Make sure to cite completely all sources used.



FunWork #1 ---Submit only html or pdf file of your MATLAB m-file prepared using the cell mode. Use the publish button in the toolbar to obtain an html file, or go to the workspace and type

publish('your m-file name without extension','pdf')

to obtain a pdf file. Submit either html or pdf file.



·         Here is a YouTube video about hypothyroidism related to the modeling of this assignment.


·         American Thyroid Association (ATA) Hypothyroidism Booklet


·         Three fun to read papers on modeling endocrine systems:


·         L. Danziger and G. L. Elmergreen 1954 paper



·         L. Danziger and G. L. Elmergreen 1956 paper



·         L. Danziger and G. L. Elmergreen 1957 paper


·         HPA-HPT axes interconnections


·         Some papers on modeling hypothalamus-pituitary-adrenal/thyroid axes:


·         Thyroid-pituitary axis model with delays


·         Modeling the hypothalamus-pituitary-adrenal axis: A review and extension


·         Dynamics of a simplified HPT model with delays


·         Patient specific modeling of the HPA axis related to clinical diagnosis


·         Effects of the HPA axis dysregulation


·         Modeling the hypothalamus-pituitary-thyroid (HPT) axis


·         HPA/HPT axes interactions


·         Implications of HPA and HPT axes interactions


·         HPA model based human stress estimation


·         Manual for solving delay differential equations with MATLAB’s dde23


·         A model of intelligent controller for hypothyroidism treatment




·        Alternative FunWork #1

·        FunWork #2

·        FunWork #3

·        FunWork #4

·        FunWork #5



·        Midterm #1

·        Midterm #2

·        Final Exam


Grading Policy

There will be two midterm exams from the material covered in class. Each midterm will be worth 100 points. The final exam will be worth 200 points. FunWork assignments will be averaged out to be worth 200 points. The course grade will be based on 600 points.


A, A+

























In order to receive consideration, all requests for re-grades, regardless of type, will have to be submitted within one week of the return of the exam or homework in question.


Exam Schedule

Midterm Exam #1

Thursday, February 22 in EE 226; 09:00--10:15am

Midterm Exam #2

Thursday, April 21 in EE 226; 09:00--10:15am

Final Exam



FunWork Schedule

FunWork #1

Thursday, February 03

FunWork #2

Thursday, March 03

FunWork #3

Thursday, March 10

FunWork #4

Thursday, March 24

FunWork #5

Thursday, April 28



This page last updated on February 23, 2022