  Recent development of contraction theory based analysis of singularly
perturbed system has opened the door for inspecting differential behavior of
multi time-scale systems. In this paper a contraction theory based framework is
proposed for stabilization of singularly perturbed systems. The primary
objective is to design a feedback controller to achieve bounded tracking error
for both standard and non-standard singularly perturbed systems. This framework
provides relaxation over traditional quadratic Lyapunov based method as there
is no need to satisfy interconnection conditions during controller design
algorithm. Moreover, the stability bound does not depend on smallness of
singularly perturbed parameter. Combined with high gain scaling, the proposed
technique is shown to assure contraction of approximate feedback linearizable
systems. These findings extend the class of nonlinear systems which can be made
contracting.
