Ellipsoidal Toolbox (ET)

Implementation of the ellipsoidal calculus and ellipsoidal methods for reachability analysis.

Ellipsoidal Toolbox (ET) is a set of easy-to-use configurable MATLAB routines to perform operations with ellipsoids and hyperplanes of arbitrary dimensions. It computes the external and internal ellipsoidal approximations of geometric (Minkowski) sums and differences of ellipsoids, intersections of ellipsoids and intersections of ellipsoids with halfspaces and polytopes; distances between ellipsoids, between ellipsoids and hyperplanes, between ellipsoids and polytopes; and projections onto given subspaces.

Ellipsoidal methods are used to compute forward and backward reach sets of continuous- and discrete-time piecewise affine systems. Forward and backward reach sets can be also computed for piecewise linear systems with disturbances. It can be verified if computed reach sets intersect with given ellipsoids, hyperplanes, or polytopes.

The toolbox provides efficient plotting routines for ellipsoids, hyperplanes and reach sets