Given a general local differentiable family of pairs of matrices, we obtain a local differentiable family of feedbacks solving the pole assignment problem, that is to say, shifting the spectrum into a prefixed one. We ...

Given the set of square matricesM⊂Mn+m(C) that keep the subspace W = Cnx{0} ⊂ Cn+m invariant, we obtain the implicit form of a miniversal deformation of a matrix a∈M, and we compute it explicitely when this matrix is ...

Given the set of vertical pairs of matrices M¿ Mm,n(C)×Mn(C) keeping the subspace Cd×{0} ¿ Cn invariant, we compute miniversal deformations of a given pair when it is observable and the subspace Cd × {0} is marked. ...

Given S an (A,B)-invariant subspace, we prove that the set of friend feedbacks is a linear variety, which can be considered as the direct sum of the feedbacks of the restriction to S and the co-restriction to S ⊥. In ...

Given a family of linear systems depending on a parameter varying in a differentiable manifold, we obtain sufficient conditions for the existence of a (global or local) differentiable family of controllers solving the ...

Given the set of matrix pairsM Mm,n.C/ Mn.C/ keeping a subspace S Cn invariant, we obtain a miniversal deformation of a pair belonging to an open dense subset ofM. It generalizes the known results when S is a ...

It is well known that, when a full rank observable pair (C,A) is slightly perturbed, the new observability indices k′ are majorized by the initial ones k, k≻k′. Conversely, any indices k′ majorized by k can be obtained by ...

We tackle the obtaining of canonical forms for classifying linear control systems with regard to changes in the state variables. Although it was solved in the 1980s for controllable systems, it is still an open problem for ...

Specific algorithms, such as those involving the supremal of the invariant subspaces contained in a suitable subspace, are known to be able to test whether a disturbance decoupling problem (DDP) is solvable. Here, by ...