There are slides available in Khalil's website that cover the material in the syllabus (see sakai website and my separate course website). I may use the slides as a way to structure the discussion, with blackboard for details. I am placing all the slides as one big file in the Sakai, under "Resources".
My textbook "Mathematical Control Theory: Deterministic Finite Dimensional Systems. Second Edition, Springer, New York, 1998." is the one that I have used in the past, when the audience was mostly mathematics students. The book is available freely online, and could be used for additional reading. The style of the course, however, will be very different - far less abstract than my book - and will focus on nonlinear control design, which is only a small part of my own book.
Summary of topics covered, in rough order; files are found in "resources"; see sakai
introduction
resource: "khalil_book_41lectures.pdf" (lectures 1-2)
existence and uniqueness for ODE's
resource: chapter 3 of book, blackboard
2D linear phase planes
resource: "khalil_book_41lectures.pdf" (lecture 3)
linearization
resource: "khalil_book_41lectures.pdf" (lecture 4)
bifurcations
resource: "khalil_book_41lectures.pdf" (lecture 6)
stability and Lyapunov functions
resource: "khalil_book_41lectures.pdf" (lectures 7,8,9,10, and part of 11)
KL characterization of GAS
resources: "proof_k_kl_estimates.pdf" (Khalil, extracted from book)
"alpha(||x||) < V(x) proof"
"khalil_book_41lectures.pdf" (some pages from lecture 12, start page 183)
input to state stability (using notes from a summer school short course)
resource: "slides for ISS and stabilization" (pages 46-69, skipping some]
[see also "survey paper on ISS"]
stabilization implies ISS stabilization (from a paper of mine)
resource: "sketch of proof of ISS stabilization"
norms for systems, small-gain theorem
resources: "slides on systems norms for linear systems" (from Francis et al's book)
"khalil_book_41lectures.pdf" (lecture 20, page 315)
feedback stabilization problem: continuous feedback (from the summer school notes)
resources: "khalil_book_41lectures.pdf" (lecture 25, page 407)
"slides for ISS and stabilization" (pages 3-20, skipping some)
control-Lyapunov functions, universal formula (Khalil slides)
resources: "khalil_book_41lectures.pdf" (lecture 30, page 472)
blackboard proof from my textbook, page 248
normal form, zero dynamics
resource: "khalil_book_41lectures.pdf" (lecture 22, page 360)
controller form, Lie brackets, feedback linearization
resource: "khalil_book_41lectures.pdf" (lecture 23, page 377)
stabilization by feedback linearization
resource: "khalil_book_41lectures.pdf" (lecture 26, page 424)
partial linearization, peaking, backstepping
resources: "khalil_book_41lectures.pdf" (lectures 27-28, page 436)
Lie algebra conditions for accessibility; car parking example
resource: lie_algebra_accessibility_slides_from_mct_for_577.pdf (taken from my textbook)