Mathematical Problems in Engineering

Mathematical Problems in Engineering / 2001 / Article

Open Access

Volume 7 |Article ID 740690 | https://doi.org/10.1155/S1024123X01001533

Xavier Dusser, Rabah Rabah, "On exponential stabilizability of linear neutral systems", Mathematical Problems in Engineering, vol. 7, Article ID 740690, 20 pages, 2001. https://doi.org/10.1155/S1024123X01001533

On exponential stabilizability of linear neutral systems

Received30 Aug 1999
Revised17 Oct 2000

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.

Copyright © 2001 Hindawi Publishing Corporation. 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.


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