Behavioral Inequalities

We introduce behavioral inequalities as a way to model dynamical systems defined by inequalities among their variables of interest. We claim that such a formulation enables the representation of safety-aware dynamical systems, systems with bounds on disturbances, practical design limits and operational boundaries, etc. We develop a necessary and sufficient condition for the existence of solutions to such behavioral inequalities and provide a parametrization of solutions when they exist. Finally, we show the efficacy of the proposed method in two practical examples.