Algorithmic analysis of polygonal hybrid systems, Part II: Phase portrait and tools

Polygonal differential inclusion systems (SPDI) are a subclass of planar hybrid automata which can be represented by piecewise constant differential inclusions. The reachability problem as well as the computation of certain objects of the phase portrait is decidable. In this paper we show how to compute the viability, controllability and invariance kernels, as well as semi-separatrix curves for SPDIs. We also present the tool SPeeDI+, which implements a reachability algorithm and computes phase portraits of SPDIs.