Specific modelling and simulation tools have recently emerged for the study of complex systems, allowing systematic prediction of their behaviour. In case of incomplete knowledge of the original physical system, qualitative modelling tools are preferred to quantitative ones. Starting from a hybrid control systems (HCS) framework in control engineering, this paper proposes a qualitative modelling approach for a class of piecewise linear (PL) differential systems, firstly introduced as a genetic network model and having a natural feedback structure. The thresholds limits imposed to the state variables partition the state space into open regions and the resulting qualitative model is a logical abstraction of the families of continuous trajectories mapped to this partition. Part I describes the basic general models and associated problems.

Keywords: Complex systems, Hybrid control systems (HCS), Piecewise-linear (PL) systems, Qualitative models.