Rt. Mcloskey et Rm. Murray, EXPONENTIAL STABILIZATION OF DRIFTLESS NONLINEAR CONTROL-SYSTEMS USING HOMOGENEOUS FEEDBACK, IEEE transactions on automatic control, 42(5), 1997, pp. 614-628
Citations number
60
Categorie Soggetti
Controlo Theory & Cybernetics","Robotics & Automatic Control","Engineering, Eletrical & Electronic
This paper focuses on the problem of exponential stabilization of cont
rollable, driftless systems using time-varying, homogeneous feedback.
The analysis is performed with respect to a homogeneous norm in a nons
tandard dilation that is compatible with the algebraic structure of th
e control Lie algebra. It can be shown that any continuous, time-varyi
ng controller that achieves exponential stability relative to the Eucl
idean norm is necessarily non-lipschitz, Despite these restrictions, w
e provide a set of constructive, sufficient conditions for extending s
mooth, asymptotic stabilizers to homogeneous, exponential stabilizers.
The modified feedbacks are everywhere continuous, smooth away from th
e origin, and can be extended to a large class of systems with torque
inputs. The feedback laws are applied to an experimental mobile robot
and show significant improvement in convergence rate over smooth stabi
lizers.