Flow Invariance on Stratified Domains

This paper studies conditions for invariance of dynamical systems on stratified do- mains as originally introduced by Bressan and Hong. We establish Hamiltonian conditions for both weak and strong invariance of trajectories on systems with non-Lipschitz data. This is done via the identification of a new multifunction, the essential velocity multifunction. Properties of this multifunction are investigated and used to establish the relevant invariance criteria

On the Strong Invariance Property for Non-Lipschitz Dynamics

We provide a new sufficient condition for strong invariance for differential inclusions, under very general conditions on the dynamics, in terms of a Hamiltonian inequality. In lieu of the usual Lipschitzness assumption on the multifunction, we assume a feedback realization condition that can in particular be satisfied for measurable dynamics that are neither upper nor lower semicontinuous.Comment: 15 pages, 0 figures. For this revision, the authors added a remark about an alternative nonconstructive proof of the main resul

On the Stability of a Periodic Solution of Distributed Parameters Biochemical System

International audienceThis paper studies the stability of periodic solutions of distributed parameters biochemical system with periodic input Sin(t). We prove that if Sin(t) is periodic then the system has a periodic solution that is input to state stable when small perturbations are acting on the input concentration Sin(t)

Semiconcavity of the Minimum Time Function for Differential Inclusions

To appear in Dynamics of Continuous, Discrete and Impulsive SystemsInternational audienceIn this paper we consider the Minimum Time Problem with dynamics given by a differential inclusion. We prove that the minimum time function is semiconcave under suitable hypotheses on the multifunction F

The dual arc inclusion with differential inclusions

International audienceThis paper continues our study of the minimum time problem with dynamics driven by a particular type of differential inclusion. We prove under certain assumptions that the dual arc associated to an optimal solution and the supergradient of the value function along the solution are intertwined in this new setting. We also derive new optimality conditions that contain nonsmooth features with an additional constancy condition on the Hamiltonian

SEMICONCAVITY OF THE MINIMUM TIME FUNCTION FOR DIFFERENTIAL INCLUSIONS

Abstract. In this paper we consider the Minimum Time Problem with dynamics given by a differential inclusion. We prove that the minimum time function is semiconcave under suitable hypotheses on the multifunction F