ENEE 661 - Nonlinear Control Systems (P. S. Krishnaprasad)

ENEE 661 - Nonlinear Control Systems

Spring 2005

Last Update 1:45 p.m., Thursday April 21 2005

Course Information

Special Announcements

(12) Lecture Notes 9 and 10 posted

(11) Homework Set # 8 is posted. Do not forget reading assignments.

(10) Lecture 6, 7, 8 posted. Homework 7 posted (due April 8).

(9) More lectures and Homework Assignment 6 posted (due Thursday March 31)

(8) Homework Assignment 5 is posted (due Tuesday March 15)

(7) Homework Assignment 4 is posted (due Tuesday March 8)

(6) Lecture 4 part (ii) and Lecture 5 part (i) posted

(5) Homework Assignment 3 posted. Lecture 4 part (i) posted in two segments. New weblinks added.

(4) Homework Assignment 2 posted.

(3) Lecture 3 posted.

(2) Lecture 2 and Homework Set 1 posted.

(1) Lecture 1 posted.

Weekly Lecture Notes by P. S. Krishnaprasad

Lecture 1 (what is nonlinear behavior?)

Lecture 2 (planar systems, Hartman-Grobman theorem, Poincare-Bendixson theorem)

Lecture 3 (index of a plane vector field, elements of bifurcations)

Lecture 4, part (i), pages 1-9 (Banach's fixed point theorem, application to ODE's)

Lecture 4, part (i), pages 10-17 (more on the Cauchy-Lipschitz existence and uniqueness theorem)

Lecture 4, part (ii) (some concepts and theorems from elementary analysis)

Lecture 5, part (i) (stability of equilibria, basic theorems of Lyapunov and related results)

Lecture 5, part (ii) (on instability) corrections to page 2

Lecture 6 part (i) (stability in time-varying systems)

Lecture 6 part (ii) (time-varying linear systems, a converse Lyapunov theorem, Floquet theory of periodic linear systems)

Lecture 6 part (iii) (indirect method of Lyapunov)

Lecture 6 - additional reading (exponential stability and its converse)

Lecture 7 (input-output stability)

A detour on measure

Lecture 8 (absolute stability, the Lure' problem, positive real lemma)

Lecture 8 (absolute stability, circle criterion, Popov criterion, multipliers)

Lecture 9 (center manifold reduction)

Lecture 10 (feedback linearization)


Homework Assignments

Problem Set 1

Problem Set 2

Problem Set 3

Problem Set 4

Problem Set 5

Problem Set 6

Problem Set 7

Problem Set 8


Homework solutions:

For Matlab problems please remember to include your code, too.

Problem Set 1

You may get 10 extra points to explain whether the minimality condition in problem 1.11 is needed or not and where it has been used!. Your answer should be handed in with HW#3.

Problem Set 2


Some interesting resources on the web

My lecture notes on Optimal Control

Real Analysis material useful throughout the course

About Stefan Banach

About A. M. Lyapunov

About G. D. Birkhoff