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

ENEE 661 - Nonlinear Control Systems

Spring 2008

Last Update January 21, 2008

Course Information

Special Announcements

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. --------------------------------------------------------------------

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