## Homogeneous approximation, recursive observer design, and output feedback.(English)Zbl 1165.93020

Summary: 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 integrators. Combining these two tools, we propose a new global asymptotic stabilization result by output feedback for feedback and feedforward systems.

### MSC:

 93B51 Design techniques (robust design, computer-aided design, etc.) 93B52 Feedback control 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93D15 Stabilization of systems by feedback 34D20 Stability of solutions to ordinary differential equations
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