While early research on real-time systems was concerned with avoiding missed deadlines, current efforts have addressed general scheduling techniques in order to improve the overall performance when temporal requirements are satisfied. Most of these techniques are proposed based on both a deep knowledge of the system and a great deal of simulations under different workload conditions. However, no mathematical analysis has been done in order to state the reasons of these approaches and the lack of a general control method. In this paper we get a statespace model of a real-time system from which its nonlinearity is shown and the necessity of adaptive scheduling mechanisms oriented to specific applications inferred.