We introduce two new tools that can be useful in nonlinear observer and
output feedback design. The first one is a simple extension of the notion of
homogeneous approximation to make it valid both at the origin and at infinity
(homogeneity in the bi-limit). Exploiting this extension, we give several
results concerning stability and robustness for a homogeneous in the bi-limit
vector field. The second tool is a new recursive observer design procedure for
a chain of integrator. Combining these two tools, we propose a new global
asymptotic stabilization result by output feedback for feedback and feedforward
systems