Technical Report 2003-042

Invariance Kernels of Polygonal Differential Inclusions

Gerardo Schneider

August 2003

Polygonal hybrid systems are a subclass of planar hybrid automata which can be represented by piecewise constant differential inclusions (SPDIs). Here, we identify and compute an important object of SPDIs' phase portrait, namely invariance kernels. An invariant set is a set of initial points of trajectories which keep rotating in a cycle forever and the invariance kernel is the largest of such sets. We show that this kernel is a non-convex polygon and we give a non-iterative algorithm for computing the coordinates of its vertices and edges.

Note: Updated October 2003

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