**Chapter 1:** The material on second-order systems is taken out.

**Chapter 2: **This is a new chapter that gathers the material on
second-order systems which was covered in Chapters 1 and 7 of the 2^{nd}
Ed. Sections 2.1 to 2.5 belong to the first group and Section 2.6 belongs
to the second group. The chapter has also a new section (2.7) on bifurcation.
The material in Section 2.6 has been re-written in an easier style that
matches the level of an early chapter.

**Chapter 3 (2 in 2 ^{nd} Ed): **The section on mathematical
preliminaries has been moved to an appendix. The proof of the existence
and uniqueness theorem has been moved to an appendix so that students do
not have to deal with the contraction mapping principle in such early chapter.
The chapter now is much easier to read compared to the 2

**Chapter 4 (3 in 2 ^{nd} Ed): **The first three sections
on autonomous systems remain basically the same. The material on nonautonomous
systems has been rewritten to make it more accessible. First, comparison
functions are treated in a separate section (4.4). Second, the section
on nonautonomous system (4.5) has been rewritten to make it easier to read.
The basic theorem has been restated in three theorems covering different
cases and a sketch was added to illustrate the proof. In the section on
converse Lyapunov theorems (4.7), a new theorem was added to cover the
case of autonomous systems. The theorem is known as Kurzweil's theorem
and provides a Lyapunov function that approaches infinity as the trajectory
approaches the boundary of the region of attraction. It is a useful theorem
that was used recently by several researchers. It is used later in the
book to sharpen some of the results on perturbed systems and perturbations.
It is also used in the proof of the nonlinear separation principle in Chapter
14. The chapter has two new sections (4.8 & 4.9) which show how Lyapunov's
method can be used to show boundedness, ultimate boundedness, and input-to-state
stability. In the 2

**Chapter 5 (6 in 2 ^{nd} Ed): **With the changes at the end
of Chapter 4, it is now possible to teach input-output stability right
after Lyapunov stability. The small-gain theorem has been added to the
chapter, so that the chapter actually reads as if we are building the tools
to state the small-gain theorem. The chapter is the first of three chapters
that form a part of the book that deals with analysis of feedback systems.

**Chapter 6 (Section 10.3 in 2 ^{nd} Ed): **This chapter is
an expanded treatment of passivity compared to the 2

**Chapter 7 (Sections 10.1 & 10.4 in 2 ^{nd} Ed): **This
chapter gathers the classical tools which use frequency-domain analysis
of the feedback connection of a linear time-invariant system with a static
nonlinearity. Section 7.1 covers the circle and Popov criteria and Section
7.2 covers the describing function methods. The derivation of the circle
and Popov criteria makes use of the passivity and loop transformation tools
of the previous chapter. The results are more general than those of the
2

**Chapter 8 (4 in 2 ^{nd} Ed): **The chapter stays almost
the same except that a new section on stability of periodic solutions was
added (it was in Chapter 7 of the 2

**Chapter 9 (5 in 2 ^{nd} Ed): **The chapter stays almost
the same, except that the material on ultimate boundedness and input-to-state
stability has been moved to Chapter 4. In the section on continuity of
solutions (9.4), the result has been made nonlocal by combining local exponential
stability with non-local/global uniform asymptotic stability.

**Chapter 10 (8 in 2 ^{nd} Ed): **The structure of the chapter
has been changed. It is now closer to its structure in the 1st Ed. In particular,
the section on periodic perturbation of autonomous systems (10.3) was brought
back and most of the proofs are given within the text rather than in the
appendix. The perturbation and averaging theorems on the inifinite-time
interval have been stated as nonlocal results by combining local exponential
stability with non-local/global uniform asymptotic stability.

**Chapter 11 (9 in 2 ^{nd} Ed): **The chapter stays the same
as in the 2

**Chapter 12 (11 in 2 ^{nd} Ed): **The chapter stays the same
with one exception: integral control has been emphasized and treated in
a separate section (12.2) by discussing the principle of integral control
of a general nonlinear system, irrespective of the stabilizing feedback
control technique. New results on gain scheduling are given in two theorems.
In the 2

**Chapter 13 (12 in 2 ^{nd} Ed): **This chapter on feedback
linearization has seen major changes. In the 2

**Chapter 14 (13 in 2 ^{nd} Ed): **The chapter retains the
sections on sliding mode control, Lyapunov redesign and backstepping from
the 2