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

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

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 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

The analysis of exact controllability of neutral type systems by the moment problem approach

Presented also at the 47th IEEE CDCInternational 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. Key words. neutral-type systems, exact controllability, moment problem, Riesz basis, distributed delays AMS subject classifications. 93B05, 93C23, 93C25 DOI. 10.1137/060650246 1