Sharp partial order and linear autonomous systems

Abstract This paper deals with autonomous linear systems and the sharp partial order. Given an autonomous linear system, we find another system, which is related to the first one by means of the sharp partial order. This relation can be interpreted in different ways: as a perturbation or as a projection of the initial system. Both points of view allow us to work with a new system with some previously selected behaviour. The solutions of the two systems are related via a matrix that gives the gap between them. We design some algorithms and analize their performance with numerical examples.