In this paper, we introduce two distinct types of nonlinear dynamical
systems, T1 and T2, both of which possess a triangular structure. It i
s shown that all systems belonging to T1 can be made stable and that i
f they belong to a subclass T1s, the stability holds globally. A preci
se characterization of the general class of nonlinear systems transfor
mable to T1 is carried out. The second class, T2, corresponds to a set
of second-order nonlinear differential equations and is motivated by
problems that occur in mechanical systems. It is shown that global tra
cking can be achieved for all systems in T2. A constructive approach i
s used in all cases to develop the adaptive controller, and both stabi
lization and tracking are shown to be realizable. Simple examples are
given to illustrate the different classes of nonlinear systems as well
as the idea behind the approach used to stabilize them.