External polyhedral estimates of reachable sets of linear and bilinear discrete-time systems with integral bounds on additive terms

Abstract

The paper concerns the reachability problem for linear and bilinear discrete-time systems for the case when additive input terms are restricted by integral non-quadratic con-straints and initial states are restricted by parallelepiped-valued ones. The bilinearity is caused by the fact that interval bounds on the coefficients of the system are imposed. Algorithms for constructing external parallelepiped-valued (shorter, polyhedral) estimates of reachable sets are presented.