Hybrid Abstractions of Affine Systems

This paper considers the problem of building a set of hybrid abstractions for affine systems in order to compute over approximations of the reachable space. Each abstraction is based on a partition of the continuous state space that is defined by hyperplanes generated by linear combinations of two vectors. The choice of these vectors is based on considerations on the dynamics of the system and uses, for example, the left eigen vectors of the matrix that defines this dynamics. It is shown how the reachability calculus can then be performed on a composition of such abstractions and how its accuracy depends on the choice of hyperplanes that defines the abstraction but also on the number of abstractions that are composed.