ON CONTROL OF 2D SWITCHED SYSTEMS BY MEANS OF GEOMETRIC ALGEBRA FOR CONICS
Anna Derevianko -- Brno University of Technology
The paper deals with an algorithm for control of a linear switched system by means of Ge- ometric Algebra. More precisely, we develop a switching path searching algorithm for a two–dimensional linear dynamical switched system with non–singular matrix. Then it is nat- ural to represent them as elements of Geometric Algebra for Conics (GAC) and construct the switching path by calculating the switching points, i.e. intersections and contact points. For this, we use symbolic algebra operations, more precisely the wedge and inner products, that are realisable by sums of products in the coordinate form. This choice guarantees optimality of the switching path with respect to the number of switches. On two examples we demonstrate the search for conics’ intersections and, consequently, we describe a construction of a switching path in both cases.