Homogeneity in the bi-limit as a tool for observer and feedback design

Abstract-- We introduce an 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, robustness and uniform (in the initial condition) finite time convergence for a homogeneous in the bi-limit vector field. We then introduce a homogeneous in the bi-limit observer and state-feedback for a chain of integrators. Combining these two tools we establish a global asymptotic stabilization result by output feedback for feedback and feedforward systems. We obtain also a finite time observer for globally Lipschitz system.

• Type: Journal
• Year: 2009
• Where: CDC
• Authors: Vincent Andrieu, Laurent Praly, Alessandro Astolfi
• Keywords: CDC 2009, Control Systems, Finite Time, Finite Time Convergence, Finite Time Observer