Approximating switched continuous systems by rectangular automata

An approximation procedure is presented for a class of hybrid systems in which switching occurs only when the continuous state trajectory crosses thresholds defined by a rectangular partitioning of the state space. The result of the approximation are rectangular automata, a class of hybrid automata for which a numerically robust approximative analysis algorithm exists. Thus, the approximation procedure can be applied when we are interested in the reachability set of a switched continuous system for which a direct analysis is infeasible. The approach is illustrated by application to a simple physical example. As an extension, an algorithm is presented to adjust the accuracy of the approximation to the continuous dynamics by choosing a state space partitioning according to the variation of the vector field.