ENEE 660 - System Theory (P. S. Krishnaprasad)

ENEE 660 - System Theory

Fall 2010

Last Update Monday, December 13, 2010, 12:00 noon

Course Information

Special Announcements (in reverse chronological order)

(10) Completed postings (notes, HW 8, Midterm II)

(9) Homework Set 7 posted.

(8) Lecture notes on eigenvalue placement theorem, optimality, observability, and observer-controller method for stabilization posted.

(7) Problem Set 6 has been posted. Solutions to Mid Term Exam I and Homework Set 5 emailed.

(6) Lecture 3(b) and Problem Set 5 posted.

(5) Reading assignment from Textbook: Ch. 5 - solving linear time varying systems

(4) Problem set 2 is assigned (below).

(3) Website for textbook (errata + practice)

(2) Reading assignment from Textbook: Ch 1 (for notation); Ch 2 (for motivation); Ch 7 (for Jordan normal form)

(1) Completed first homework set is due back in class on Thursday, September 9, 2010.

Weekly Lecture Notes by P. S. Krishnaprasad

Lecture 0 (highlights of what this class is about)

Lecture 1(a) (very basic linear algebra) Lecture 1(b) (spectrum, linear o.d.e.)

Lecture 2(a) (linear differential equations and transition matrices)Lecture 2(b) (properties of transition matrices)

Lecture 3(a) (linear differential equations with inputs; and adjoints of linear maps) Lecture 3(b) (reachability and control canonical form)

Lecture 4(a) (eigenvalue/pole placement theorem; proof by Heymann-Hautus approach in multi-input setting) Lecture 4(b) (reachability, orthogonality and optimality) Lecture 4(c) (Observability, Luenberger observer, stabilization by observer-controller design)

Lecture 5 (notes from Brockett FDLS on Floquet Theory - emailed to class)

Lecture 6 (notes from Brockett FDLS on Realization Theory, time domain - emailed to class)

Lecture 7 (notes from Brockett FDLS on Realization Theory, frequency domain - emailed to class)

Lecture 8 (paper of Pavol Brunovsky, Classification of Controllable Systems - emailed to class)

Lecture 9 (notes on Kronecker invariants)

Lecture 10a (polynomial division, gcd, Bezout equation)

Lecture 10b (frequency domain observer-controller design)

A question related to Lecture 6 --------------------------------------------------------------------

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



Mid Term I

Mid Term II



Homework solutions are sent by email.

For Matlab problems, include your code.


Some resources on the web

My lecture notes on Optimal Control

Website for Feedback Systems: An Introduction for Scientists and Engineers by K. J. Astrom and R. M. Murray On-line readable book

Real Analysis Book by Cinlar and Vanderbei - material useful in Systems courses

About Stefan Banach

About A. M. Lyapunov

About G. D. Birkhoff