Using MATLAB toolbox “GBT” in identification and control

The Geometric Bounding Toolbox (GBT) is a set of routines in MATLAB to perform operations on polytopes, polyhedra and ellipsoids. The merit of the package is efficiency and ease of use of its routines which make these otherwise sometimes complex operations a children´s game. The geometric objects have a single name and no details of specifications have to be remembered. It is not meant that the above operations could not be performed in some other ways, but probably with much more work involved. The numerical procedures have been selected according to one of the criteria: either for their best numerical properties or for the sake of elegance. The speed and usefulness of the package is not difficult to appreciate: there is an increasing number of areas of control and digital signal processing where operations with polytopes, ellipsoids and other geometric bodies play an increasing role. Design of robust and adaptive filters and controllers might need the calculation of parameter or state regions in the forms of polytopes, ellipsoids and rectangular boxes. Also linear optimisation, numerically robust and stable computations, computational complexity are potential areas of applications. The authors illustrate how some of the routines can be used