Existence and uniqueness of the solutions of continuous nonlinear 2D Roesser Models: The globally Lipschitz case

This communication deals with a long standing open problem in the field of multidimensional systems. We tackle the question of the existence and uniqueness of the solutions for nonlinear continuous 2D Roesser models. It is proved that if the function describing the Roesser model is globally Lipschitz, a continuous solution exists and is unique for a given set of initial conditions. Several examples show that these assumptions cannot be easily relaxed. This is an important basis that is crucial to the analyzes of stability and stabilization of nonlinear Roesser models.