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IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences 2008 E91-A(5):1274-1277; doi:10.1093/ietfec/e91-a.5.1274
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Copyright © 2008 The Institute of Electronics, Information and Communication Engineers

Regular Section -- Letters -- Systems and Control

A Global Stability Analysis of a Class of Nolinear Time-Delay Systems Using Continued Fraction Property*

Joon-Young CHOI1,2

1 The author is with the Department of Electronic and Electrical Engineering, Pusan National University, 30, Jangjeon-dong, Geumjeong-gu, Busan, 609-735, South Korea. E-mail: jyc{at}pusan.ac.kr, 2 Corresponding author.


  Abstract

We consider a class of nonlinear time delay systems with time-varying delays, and achieve a time delay independent sufficient condition for the global asymptotic stability. The sufficient condition is proved by constructing a continued fraction that represents the lower and upper bound variations of the system trajectory along the current of time, and showing that the continued fraction converges to the equilibrium point of the system. The simulation results show the validity of the sufficient condition, and illustrate that the sufficient condition is a close approximation to the unknown necessary and sufficient condition for the global asymptotic stability.

Key Words: nonlinear time delay systems, global asymptotic stability, continued fraction

Manuscript received November 9, 2007. Manuscript revised January 22, 2008.

* This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2007-331-D00256).


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