2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221965We 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.Optimization and Control93B51, 93B52, 93D05, 93D15, 34D20text