Exploiting the eigenstructures of linear systems to speed up reachability computation

ABSTRACT. Reachability analysis has recently proved to be a useful technique for analyzing the behaviors of under-specified biological models. In this paper, we propose a method exploiting the eigenstructure of a linear continuous system to efficiently estimate a bound on the time the system can reach a target set from an initial set. This estimation can be then directly integrated in an existing algorithm for hybrid systems with linear continuous dynamics, to speed up reachability computations. Furthermore, it can also be used to improve time-efficiency of the hybridization technique that is based on a piecewise-linear approximation of non-linear continuous dynamics. The proposed method is illustrated on a number of examples including a biological model.