Exact observability and controllability for linear neutral type systems

The problem of exact observability is analyzed for a wide class of neutral type systems by an infinite dimensional approach. The duality with the exact controllabil-ity problem is the main tool. It is based on an explicit expression of a neutral type system which corresponding to the abstract adjoint system. A nontrivial relation is obtained between the initial neutral system and the system obtained via the adjoint abstract state operator. The characterization of the duality between controllability and observability is deduced, and then observability conditions are obtained.Comment: Accepted in Systems and Control Letter

Stability, stabilizability and exact controllability of a class of linear neutral type systems

Linear systems of neutral type are considered using the infinite dimensional approach. The main problems are asymptotic, non-exponential stability, exact controllability and regular asymptotic stabilizability. The main tools are the moment problem approach, the Riesz basis of invariant subspaces and the Riesz basis of family of exponentials.Comment: Conf\'erence pl\'eni\`er

Spectral assignment for neutral-type systems and moment problems.

International audienceFor a large class of linear neutral-type systems the problem of assigning eigenvalues and eigenvectors is investigated, i.e. finding the system that has the given spectrum and, in some sense, allmost all eigenvectors. The solution of this problem enables vector moment problems to be considered using the construction of a neutral-type system. The exact controllability property of the system obtained gives the solution of the vector moment problem

On a vector moment problem arising in the analysis of neutral type systems

5 pagesInternational audienceThe solvability of some new vector moment problem related with the exact controllability of neutral type systems is investigated. Condition of equivallence of this problem with the controllability of some system is analyzed. The time of solvability is precised

On a vector moment problem appearing in the analysis of controllability of neutral type systems

International audienceWe consider the solvability of a vector moment problem associating it to the analysis of controllability for a certain delayed system of neutral type. In this way we succeeded to determine exactly the minimal interval on which the moment problem is solvable

Eigenvalues and eigenvectors assignment for neutral type systems

International audienceFor a class of linear neutral type systems the problem of eigenvalues and eigenvectors assignment is investigated, i.e. finding the system which has the given spectrum and almost all, in some sense, eigenvectors. The result is used for the analysis of the critical number of solvability of a vector moment problem

Exact controllability of linear neutral type systems by the moment problem approach

International audienceThe problem of exact null-controllability is considered for a wide class of linear neutral type systems with distributed delay. The main tool of the analysis is the application of the moment problem approach and the theory of the basis property of exponential families. A complete characterization of this problem is given. The minimal time of controllability is specified. The results are based on the analysis of the Riesz basis property of eigenspaces of the neutral type systems in Hilbert space

Observability and controllability for linear neutral type systems

International audienceFor a large class of linear neutral type systems which include distributed delays we give the duality relation between exact controllability and exact observability. This duality is based on the representation of the abstract adjoint system as a special neutral type system. As a consequence of this duality relation, a characterization of exact observability is obtained. The time of observability is precised

On a class of strongly stabilizable systems of neutral type

International audienceWe consider the strong stabilizability problem for delayed system of neutral type. For simplicity the case of one delay in state is studied. We separate a class of such systems and give a constructive solution of the problem in this case, without the derivative of the localized delayed state. Our results are based on an abstract theorem on the strong stabilizability of contractive systems in Hilbert space. An illustrating example is also given