Matemàtica Aplicada 1

A generalized Sylvester matrix equation is considered. This equation is related with the stabilizer of a triple of matrices under the Lie group action on the space of triples of matrices which corresponds to the equivalence relation generalizing, in a natural way, the similarity between square matrices.criterion for the structural stability of a triple of matrices t is deduced in

ABSTRACT We present a geometric approach to the study of singular switched linear systems, defining a Lie group action on the differentiable manifold consisting of the matrices defining their subsystems with orbits coinciding with equivalence classes under an equivalence relation which preserves reachability and derive miniversal (orthogonal) deformations of the system. We relate this with some new results on reachability of such systems.

A generalized Sylvester matrix equation is considered. This equation is related with the stabilizer of a triple of matrices under the Lie group action on the space of triples of matrices which corresponds to the equivalence relation generalizing, in a natural way, the similarity between square matrices.criterion for the structural stability of a triple of matrices t is deduced in