SimplicialVIEW, a package for robust stability analysis.

SimplicialVIEW is a package that implements the simplicial approximation theorem of combinatorial topology using computational geometry for the purpose of visualizing the regions of stability/instability in the parameter space of a robust control problem. The space of uncertainty is approximated by a polyhedron invoking Alexandroff's theorem, the vertices of the polyhedron are mapped to the complex plane using the usual Nyquist map, and the Horowitz template is triangulated using the Voronoi diagram/ Delauney triangulation. The unique simplex of the triangulation of the template that contains 0 is identified, the polyhedron of uncertainty is refined , until a simplicial map can be constructed. Once a simplicial map between the uncertainty and the template is achieved, computing the pre-image of the simplex containing the origin of the complex plane yields an assembly of simplexes that provides an approximation of the crossover.
Prof E Jonckheere (University of Southern California)