Interval methods for simulation of dynamical systems with state-dependent switching characteristics

In this paper, an interval arithmetic simulation algorithm is introduced for simulation of continuous-time systems with state-dependent switchings between different dynamical models. For that purpose, the conditions for all possible transitions between these models have to be evaluated during simulation to determine the switching times and hence to obtain guaranteed enclosures for all state variables. In contrast to other simulation techniques, all system parameters are defined as interval variables to analyze the effect of uncertainties on the switching times and the dynamical behavior of the complete system.