Lasalle's Invariance Theorem for Nonsmooth Lagrangian Dynamical Systems

Sophie Chareyron (1) , Pierre-Brice Wieber (1)

1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems

A key condition for the statement of Lasalle's invariance theorem is the continuity of the trajectories of the dynamical systems with respect to initial conditions. Systems with discontinuous flows generally don't present such a continuity, but in the particular case of nonsmooth Lagrangian dynamical systems we will see that in fact this continuity property holds in most cases. We will then be able to propose a a LaSalle's invariance theorem for nonsmooth dynamical systems satisfying this property through the use of general time-invariant flows.orem for nonsmooth dynamical systems still needs to be stated, so we propose here to extend this theorem through the framework of nonsmooth dynamical systems.

Domaines: Robotique [cs.RO]; Automatique

Sophie Chareyron, Pierre-Brice Wieber. Lasalle's Invariance Theorem for Nonsmooth Lagrangian Dynamical Systems. Euromech Nonlinear Dynamics Conference, 2005, Eindhoven, Netherlands. ⟨inria-00390416⟩