Brief Discontinuous exponential stabilization of chained form systems

Authors:
Nicolas Marchand;Mazen Alamir
Affiliations:
Laboratoire d'Automatique de Grenoble, INPG-CNRS UMR 5528, ENSIEG BP 46, 38402 St Martin d'Hères Cedex, France;Laboratoire d'Automatique de Grenoble, INPG-CNRS UMR 5528, ENSIEG BP 46, 38402 St Martin d'Hères Cedex, France
Venue:
Automatica (Journal of IFAC)
Year:
2003

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Abstract

In this paper a novel approach to exponential stabilization of chained form system is proposed. Provided that the control law fulfills mild assumptions, it is shown that a Brunovsky-like change of coordinates depending on the control transforms any chained form system into a system having a linearly bounded nonlinear part. Using linear tools, it is possible to exponentially stabilize a chained form system for any initial condition outside a submanifold containing the origin. This result is then generalized to global exponential stabilization. The so obtained static discontinuous feedback is bounded for bounded states and exponentially converges to zero along the closed-loop trajectories of the system.