Title :
Homogeneity in the bi-limit as a tool for observer and feedback design
Author :
Andrieu, Vincent ; Praly, Laurent ; Astolfi, Alessandro
Author_Institution :
LAAS-CNRS, Univ. of Toulouse, Toulouse, France
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.
Keywords :
approximation theory; convergence of numerical methods; feedforward; nonlinear systems; observers; state feedback; bi limit observer; bi limit vector field; feedback design; feedback systems; feedforward systems; finite time convergence; global asymptotic stabilization; globally Lipschitz system; homogeneous approximation; observer design; output feedback; state feedback; Control systems; Convergence; Feedforward systems; H infinity control; Linear feedback control systems; Nonlinear control systems; Nonlinear systems; Output feedback; Polynomials; Robust stability;
Conference_Titel :
Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on
Conference_Location :
Shanghai
Print_ISBN :
978-1-4244-3871-6
Electronic_ISBN :
0191-2216
DOI :
10.1109/CDC.2009.5400263