A Grobman-Hartman Theorem for Control Systems

Laurent Baratchart (1) , Monique Chyba (2) , Jean-Baptiste Pomet (1)

1 APICS - Analysis and Problems of Inverse type in Control and Signal processing
2 Department of Mathematics [Hawaii]

We consider the problem of locally linearizing a control system via topological transformations. According to [2, 3], there is no naive generalization of the classical Grobman-Hartman theorem for ODEs to control systems: a generic control system, when viewed as a set of underdetermined differential equations parametrized by the control, cannot be linearized using pointwise transformations on the state and the control values. However, if we allow the transformations to depend on the control at a functional level (open loop transformations), we are able to prove a version of the Grobman-Hartman theorem for control systems.

Domaines: Optimisation et contrôle [math.OC]

Laurent Baratchart, Monique Chyba, Jean-Baptiste Pomet. A Grobman-Hartman Theorem for Control Systems. Journal of Dynamics and Differential Equations, 2006, ⟨10.1007/s10884-006-9014-5⟩. ⟨inria-00000920⟩