A new approach to stability analysis of neural networks with time-varying delay via novel Lyapunov--Krasovskii functional

doi:10.1088/1674-1056/19/5/050507

中国物理B ›› 2010, Vol. 19 ›› Issue (5): 50507-050507.doi: 10.1088/1674-1056/19/5/050507

A new approach to stability analysis of neural networks with time-varying delay via novel Lyapunov--Krasovskii functional

O.M.Kwon¹, S.M.Lee², JuH.Park³

(1)College of Electrical and Computer Engineering, 410 SungBong-Ro, Heungduk-Gu, Chungbuk National University, Cheongju 361-763, Republic of Korea; (2)Department of Electronic Engineering, Daegu University, Gyungsan, Gyungbuk 712-714, Republic of Korea; (3)Nonlinear Dynamics Group, Department of Electrical Engineering, Yeungnam University, 214-1 Dae-Dong, Kyongsan 712-749, Republic of Korea

收稿日期:2009-08-19 修回日期:2009-10-29 出版日期:2010-05-15 发布日期:2010-05-15

A new approach to stability analysis of neural networks with time-varying delay via novel Lyapunov--Krasovskii functional

S. M. Lee^a)†, O. M. Kwon^b)‡, and Ju H. Park^c)*

^a Department of Electronic Engineering, Daegu University, Gyungsan, Gyungbuk 712-714, Republic of Korea; ^b College of Electrical and Computer Engineering, 410 SungBong-Ro, Heungduk-Gu, Chungbuk National University, Cheongju 361-763, Republic of Korea; ^c Nonlinear Dynamics Group, Department of Electrical Engineering, Yeungnam University, 214-1 Dae-Dong, Kyongsan 712-749, Republic of Korea

Received:2009-08-19 Revised:2009-10-29 Online:2010-05-15 Published:2010-05-15

摘要/Abstract

摘要： In this paper, new delay-dependent stability criteria for asymptotic stability of neural networks with time-varying delays are derived. The stability conditions are represented in terms of linear matrix inequalities (LMIs) by constructing new Lyapunov--Krasovskii functional. The proposed functional has an augmented quadratic form with states as well as the nonlinear function to consider the sector and the slope constraints. The less conservativeness of the proposed stability criteria can be guaranteed by using convex properties of the nonlinear function which satisfies the sector and slope bound. Numerical examples are presented to show the effectiveness of the proposed method.

Abstract: In this paper, new delay-dependent stability criteria for asymptotic stability of neural networks with time-varying delays are derived. The stability conditions are represented in terms of linear matrix inequalities (LMIs) by constructing new Lyapunov--Krasovskii functional. The proposed functional has an augmented quadratic form with states as well as the nonlinear function to consider the sector and the slope constraints. The less conservativeness of the proposed stability criteria can be guaranteed by using convex properties of the nonlinear function which satisfies the sector and slope bound. Numerical examples are presented to show the effectiveness of the proposed method.

Key words: neural networks, Lyapunov--Krasovskii functional, sector bound, time-delay

中图分类号: (Neural networks, fuzzy logic, artificial intelligence)

07.05.Mh

02.10.Yn (Matrix theory) 02.30.Yy (Control theory) 02.60.Dc (Numerical linear algebra)

S.M.Lee, O.M.Kwon, JuH.Park. A new approach to stability analysis of neural networks with time-varying delay via novel Lyapunov--Krasovskii functional[J]. 中国物理B, 2010, 19(5): 50507-050507.

S. M. Lee, O. M. Kwon, and Ju H. Park. A new approach to stability analysis of neural networks with time-varying delay via novel Lyapunov--Krasovskii functional[J]. Chin. Phys. B, 2010, 19(5): 50507-050507.

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A new approach to stability analysis of neural networks with time-varying delay via novel Lyapunov--Krasovskii functional

A new approach to stability analysis of neural networks with time-varying delay via novel Lyapunov--Krasovskii functional

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