Hybrid modelling of a discontinuous dynamical system including switching control

Although discontinuous, non-smooth or switched dynamical systems have been broadly studied, there still exist dynamical behaviours which are not completely understood. In particular, those related to transitions between state-space regions and to crossings through discontinuity surfaces. The problem of specifying system transitions becomes crucial when multiple discontinuity surfaces or switching elements are present. In this case, a great deal of care has to be taken in order to simulate the system and to verify its properties. Obtaining a computational model appears to be an elegant way for the specification of the transitions and event-triggered phenomena involved in the dynamical behaviour of discontinuous systems. This is the goal of this paper. A class of discontinuous dynamical systems including control inputs and outputs is reinterpreted within the hybrid-automata framework, and what is referred as to discontinuous-dynamical-systemhybrid automaton is proposed.An example is used, which corresponds to a 2-degrees-of-freedom electromechanical system including discontinuous friction and sliding-mode control. This system exhibits several discontinuity surfaces which give rise to different types of transitions and dynamical behaviours. New computational-kind phenomena may arise when the system is reinterpreted as a hybrid dynamical system. Nevertheless, this paper only deals with the modelling and specification of the system.