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Mathematical Problems in Engineering
Volume 2009, Article ID 457468, 14 pages
Research Article

Output Feedback Stabilization of Linear Time-Varying Uncertain Delay Systems

1Department of Electrical and Electronic Engineering, Shinshu University, 4-17-1 Wakasato, Nagano 380-8553, Japan
2Department of Business Administration and Information, Setsunan University, 17-8 Ikeda-naka-machi, Neyagawa, Osaka 572-8508, Japan

Received 27 February 2009; Accepted 24 May 2009

Academic Editor: John Burns

Copyright © 2009 Tomoaki Hashimoto and Takashi Amemiya. 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.


This paper investigates the output feedback stabilization problem of linear time-varying uncertain delay systems with limited measurable state variables. Each uncertain parameter and each delay under consideration may take arbitrarily large values. In such a situation, the locations of uncertain entries in the system matrices play an important role. It has been shown that if a system has a particular configuration called a triangular configuration, then the system is stabilizable irrespective of the given bounds of uncertain variations. In the results so far obtained, the stabilization problem has been reduced to finding the proper variable transformation such that an 𝑀-matrix stability criterion is satisfied. However, it still has not been shown whether the constructed variable transformation enables the system to satisfy the 𝑀-matrix stability condition. The objective of this paper is to show a method that enables verification of whether the transformed system satisfies the 𝑀-matrix stability condition.