Week 
Date 
Lecture 
Topics 
1 
Sept 9 
1 
Introduction: ODEs, vector fields, dynamical systems 

Sept 11 
2 
Mathematical preliminaries 
2 
Sept 16 
3 
Mathematical preliminaries 

Sept 18 
4 
Existence and uniqueness of solutions 
3 
Sept 23 
5 
Finite escape time, continuity w.r.t. ic's, comparison lemma 

Sept 25 
6 
Invariant sets, Nagumo theorem 
4 
Sept 30 
7 
Limit sets, PoincareBendixson theorem 

Oct 2 
8 
Linearization, HartmanGrobman Theorem 
5 
Oct 7 
9 
Feedback linearization 

Oct 9 
10 
Feedback linearization 
6 
Oct 14 
11 
Thanksgiving 

Oct 16 
12 
Application: gait control of a walking robot

7 
Oct 21 
13 
Application: gait control of a walking robot


Oct 23 
14 
Lyapunov stability theory 
8 
Oct 28 
15 
BarbashinKrasovksii Theorem, Converse theorems 

Oct 30 
16 
LaSalle Invariance Principle 
9 
Nov 4 
17 
Midterm Exam 

Nov 6 
18 
Stability of linear systems 
10 
Nov 11 
19 
Obstruction to continuous feedback stabilization 

Nov 13 
20 
Backstepping 
11 
Nov 18 
21 
Backstepping 

Nov 20 
22 
Adaptive control 
12 
Nov 25 
23 
Adaptive control 

Nov 27 
24 
TBA 
13 
Dec 2 
25 
TBA 