Some results on the behavior of Lipschitz continuous systems

This paper is devoted to the study of the behavior of Lipschitz continuous systems. We unify and improve through the reformulation of the Lipschitz continuity of a system in terms of the dissipativity of an associated fictitious system. our previous results concerning the Lyapunov stability of unperturbed motions associated with any inputs. Moreover, we show that the Lipschitz continuous systems have the steady-state property with respect to any inputs belonging to L^e_p with p ϵ [1, ∞(i.e. their asymptotic behavior is uniquely determined by the asymptotic behavior of the input)]. Finally, we characterize the behavior of stationary Lipschitz systems for periodic and almost periodic inputs. We end the paper by a example showing that these results allow us to explain the well-known properties attached to the behavior of a controlled missile.