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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 154769, 7 pages
Research Article

An Improved Finite-Time Stability and Stabilization of Linear System with Constant Delay

Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Received 21 August 2014; Revised 15 December 2014; Accepted 16 December 2014; Published 28 December 2014

Academic Editor: Vu Ngoc Phat

Copyright © 2014 Thaned Rojsiraphisal and Jirapong Puangmalai. 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.


Practical systems in engineering fields often require that values of state variables, during the finite-time interval, must not exceed a certain value when the initial values of state are given. This leads us to investigate the finite-time stability and stabilization of a linear system with a constant time-delay. Sufficient conditions to guarantee the finite-time stability and stabilization are derived by using a new form of Lyapunov-Krasovskii functional and a desired state-feedback controller. These conditions are in the form of LMIs and inequalities. Two numerical examples are given to show the effectiveness of the proposed criteria. Results show that our proposed criteria are less conservative than previous works in terms of versatility of minimum bounds and larger bounds of time-delay.