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

Andrieu, Vincent; Praly, Laurent; Astolfi, Alessandro

SIAM J. Control Optim. 47, No. 4, 1814-1850 (2008).

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

Keywords:

homogeneous approximation; output feedback and observer