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)