Mathematical Problems in Engineering
Volume 7 (2001), Issue 1, Pages 67-86
doi:10.1155/S1024123X01001533
On exponential stabilizability of linear neutral systems
1Institut de Recherche en Communication et Cybernétique de Nantes, 1, rue de la Noë BP 92101, F-44321, Nantes Cedex 3, France
2École des Mines de Nantes, 4, rue A. Kastler, BP 20722, F-44307, Nantes Cedex 3, France
Received 30 August 1999; Revised 17 October 2000
Copyright © 2001 Xavier Dusser and Rabah Rabah. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In this paper, we deal with linear neutral functional differential systems. Using an extended state space and an extended control operator, we transform the initial neutral system in an infinite dimensional linear system. We give a sufficient condition for admissibility of the control operator B, conditions under which operator B can be acceptable in order to work with controllability and stabilizability. Necessary and sufficient conditions for exact controllability are provided; in terms of a gramian of controllability N(μ). Assuming admissibility and exact controllability, a feedback control law is defined from the inverse of the operator N(μ)
in order to stabilize exponentially the closed loop system. In this case, the semigroup generated by the closed loop system has an arbitrary decay rate.