Course Outline  
Lecture (CSI 3120):  TuTh 2:00pm  3:15pm. P. S. Krishnaprasad 
Office Hours (AVW 2233):  M 4:006:00 pm; Tu 5:107:00 pm 
Special Announcements (in reverse chronological order)11. Read material from Lecture 5, part (i) (stability of equilibria, basic theorems of Lyapunov and related results) Lecture 5, part (ii) (on instability) corrections to page 2, ALL located in the 2010 part of this website.10. Homework Set 4 posted (on Lyapunov theory) 9. Homework Set 3 posted 8. First page of Lecture 3(a) corrected (diagonal dominance and contraction). 7. Lecture 3(b) (mean value theorem) posted. Material up to and including this will be part of Mid Term I on February 24. 6. Lecture 2(b) (on Lie brackets in control  examples) posted. Homework assignment 2 posted. A practice exam will be emailed to you. 5. Lecture 3(a), on contraction mapping fixed point theorem, and existenceuniqueness theorem for ODEs posted  for Saturday class (Feb 12) 4. Lecture 2(a), a very basic introduction to matrix Lie groups and Lie algebras, is posted. Problem set 1 is posted. There will be an extra class on Saturday February 12 from 1:00 pm till 4:00 pm, most likely in room 2168, A.V. Williams building. 3. Lecture notes 1(a) is posted. Lecture notes 1(c) on an alternative way to frame a curve is posted. This will be covered in homework sets but no formal lecture will be given. Read pages 68 of Lecture 0 for a quick summary of this material. Read pages 910 of Lecture 0 for the recasting of the frame equations back into the original 't' parametrization. Show this (chain rule). 2. Read first few pages of Brockett's 1973 and 1976 papers (see OR below). 1. Look for free download (PDF) of Hans Samelson's book on Lie algebras and the expository volume on Motion, Control, and Geometry (from NAP) under Other Resources (OR) at the end of this page. Read pages 15 of Samelson carefully, and my article in the NAP volume for some motivation. This version of the class website will be under construction and update through the semester. Notes from 2010 are linked here. The new notes from 2011 will be added, starting Saturday, January 22, 2011. Copyrighted material in journals is linked below through journal websites. You can access them when logged into the umd.edu domain. 
Lecture 1 (what is nonlinear behavior?)
Lecture 2 (planar systems, HartmanGrobman theorem, PoincareBendixson theorem)
Lecture 3 (index of a plane vector field, elements of bifurcations)
Lecture 4, part (i), pages 19 (Banach's fixed point theorem, application to ODE's) Lecture 4, part (i), pages 1017 (more on the CauchyLipschitz existence and uniqueness theorem)
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 timevarying systems) Lecture 6 part (ii) (timevarying 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 (inputoutput stability)
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)



My lecture notes on Optimal Control (ENEE 664)
My lecture notes on (Linear) System Theory (ENEE 660)
Website for Feedback Systems: An Introduction for Scientists and Engineers by K. J. Astrom and R. M. Murray Online readable book
Notes on Lie Algebras by Hans Samelson A classic Roger Howe's 1983 paper (Very basic Lie theory); corrections to Howe's paper (1984)
Paper by Wei and Norman on product of exponentials representation (1964)
Motion, Control and Geometry Four expository articles illustrating nonlinear control in action
Two classic papers by Roger Brockett Lie Algebras and Lie Groups in Control Theory (1973) and Nonlinear Systems and Differential Geometry (1976)
Real Analysis Book by Cinlar and Vanderbei  material useful in Systems courses
About Sophus Lie
About Stefan Banach
About A. M. Lyapunov
About G. D. Birkhoff
