Projection and Aggregation in Maxplus Algebra
Guy Cohen, Stéphane Gaubert, Jean-Pierre Quadrat · Birkhäuser Boston eBooks · 2006
In maxplus algebra, linear projectors on an image of a morphism B parallel to the kernel of another morphism C can be built under transversality conditions of the two morphisms. The existence of a transverse to an image or a kernel of a morphism is obtained under some regularity conditions. We show that those regularity and transversality conditions can be expressed linearly as soon as the space to which Im(B) and Ker(C) belong is free and its order dual is free. The algebraic structure has these two properties. Projectors are constructed following a previous work. Application to aggregation of linear dynamical systems is discussed.