TK 8103 - Advanced Nonlinear Systems - Fall 2005

Time and place: Friday 13.15 - 15.00  Room T9 Marine Technology Centre (Tyholt)

Responsible: Prof. Olav Egeland

Instructor: Erlend Kristiansen

Teaching assistant: None

Prerequisites: Advanced calculus, matrix theory, and state-space linear systems theory

Homework: Homework will be assigned at each lecture; in order to be admitted to the exam you have to complete successfully at least 3 homeworks among homework 1 through 6, and at least 3 homeworks among homework 7 through 12. You are encouraged to do homework together, but you will have to write your own solutions.

Exam: Written final exam, Monday Dec.12th, 4 hours, all aids permitted.


Textbook: H. Khalil, Nonlinear Systems (3rd edition), Prentice Hall, 2002

Useful references:
S. Sastry, Nonlinear Systems: Analysis, Stability, and Control. Springer-Verlag, 1999 (covers approximately all the topics in the syllabus).
W. Hahn, Stability of Motion. Springer-Verlag, 1967 (useful mainly for Lyapunov stability).
A. Isidori, Nonlinear Control Systems, volume II. Springer-Verlag, 1999 (useful mainly for Lyapunov stability and passivity).

Note: On Nov.4. there will be a guest lecture on Contraction Analysis from 13.15-15.00 in T3/T4. The regular lecture will be held the same day from 10.15-12.00.


Syllabus

Lecture Date Topic Textbook sections
 Lecturer

Problems

Solutions
1
 September 8
 Introduction I
 1.1, 1.2.1, 2.2
Reading: 1.2.3, 2.1, Appendix A
 Kristiansen

#1

#1
2
 September 9
 Introduction II
 1.2.4, 2.3, 2.4
 Kristiansen

#2

#2
3
 September 16 Fundamental Properties
 3.1
 Kristiansen

#3

#3
4
 September 23 Lyapunov Stability I 4.1
 Kristiansen

#4

#4
5
 September 30
 Lyapunov Stability II 4.2, 4.3
 Kristiansen

#5

#5
6
 October 7
 Lyapunov Stability III 4.4, 4.5
Reading: 4.6
 Kristiansen

#6

#6
7
 October 14 Lyapunov Stability IV 4.7, 4.8
 Kristiansen

#7

#7
8
 October 21 Lyapunov Stability V
 4.9
 Kristiansen

#8

#8
9
 October 28 Input-Output Stability I
 5.1, 5.2 Kristiansen

#9

#9
10
 November 4
 Input-Output Stability II/ Contraction Analysis 5.3, 5.4
 Kristiansen/Jouffroy

#10

#10
11
 November 11 Passivity I
 6.1, 6.2
Reading: 6.3
 Kristiansen

#11

#11
12
 November 18 Passivity II
 6.4,  6.5
Kristiansen

#12

#12
13
 November 25 Stability of Perturbed Systems 
 9.1, 9.2
 Kristiansen

#13

#13

 

Older exams

Exam 2004, solution 2004. Exam 2003, solution 2003.

Good luck!



Editor: Erlend Kristiansen, Contact Address: Erlend.Kristiansen@ntnu.no