Empirical models that exhibit monotone responses to monotone inputs

Many physical systems exhibit monotonie responses to monotonie input sequences (e.g., monotonically increasing step responses). Given such a physical process V and a particular class C of empirical model structures, this paper considers two questions. First, can models in this class exhibit monotonie responses to monotonie input sequences and second, if they can, how must these models be constrained to guarantee this behavior? In the linear case, a complete characterization is possible that applies to both steady-state and dynamic behavior, but for nonlinear models it is important to distinguish between steady-state and dynamic monotonicity. The motivations for this investigation are empirical model structure selection (if monotone responses are desired, select a model class that can exhibit this behavior) and constrained parameter estimation (if the desired behavior is possible, what parameter constraints are required to guarantee it is achieved?).