Exploiting the eigenstructure of linear systems to speed up reachability computations

Abstract

Reachability analysis has recently proved to be a useful technique for analysing the behaviour of under-specified biological models. In this paper, we propose a method exploiting the eigenstructure of a linear continuous system to efficiently estimate a bounded interval containing the time at which the system can reach a target set from an initial set. Then this estimation can be 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.