  We design an algorithm for control of a linear switched system by means of
Geometric Algebra. More precisely, we develop a switching path searching
algorithm for a two-dimensional linear dynamical switched system with
non-singular matrix whose integral curves are formed by two sets of centralised
ellipses. Then it is natural 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. Therefore, no numerical
solver to the system of equations is needed. Indeed, the only operation that
may bring in an inaccuracy is a vector normalisation, i.e. square root
calculation. The resulting switching path is formed by pieces of ellipses that
are chosen respectively from the two sets of integral curves. The switching
points are either intersections in the first or final step of our algorithm, or
contact points. 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.
