Automatique et ordinateurs Rev. Roum. Sci. Techn. – Électrotechn. et Énerg., 54, 2, p. 205–212, Bucarest, 2009 ON QUALITATIVE BEHAVIOURS OF A CLASS OF PIECEWISE- LINEAR CONTROL SYSTEMS. PART II. A CASE STUDY VIRGINIA ECATERINA OLTEAN Keywords: Hybrid control systems (HCS), Piecewise-linear (PL) systems, Qualitative models, Simulation. Qualitative models of complex systems recently emerged as useful tools for behaviour prediction in case of incomplete system knowledge or as a variant to a difficult analytical analysis. A class of piecewise (PL) differential systems can be abstracted to a logical automaton, within a hybrid control systems (HCS) framework from control engineering, and the resulting discrete evolution provides information about the qualitative behaviours of the continuous system. The basic general models and related design problems were presented in Part I. Part II presents, within a case study, a solution to the problem of constructing a logical automaton as a discrete event abstraction of a PL differential system. Relevant qualitative evolutions are successfully checked against simulated trajectories and future research directions are proposed. 1. INTRODUCTION Starting from a piecewise-linear (PL) differential system, firstly introduced in the biological systems literature [1], this paper proposes a qualitative modelling approach, within a hybrid control systems (HCS) framework from control engineering [2]. The motivation of this model conversion problem and the two basic general models involved in the transformation are presented in the first part of the paper [3]. Summing up, the PL differential system comprises a stable linear part controlled by a nonlinear feedback law, which switches from one constant value to another, when a combination of state variables reach given threshold limits. On the other side, the HCS comprises a discrete event system (DES) that controls a continuous plant through an interface. The threshold sensors in the interface implement a partition of the continuous state space. When the continuous state reaches a partition boundary, a plant-symbol is sent to the DES controller which sends, in response, a control-symbol, instantly converted into a constant control "Politehnica" University of Bucharest, E-mail: ecaterinaoltean@yahoo.com