A delay-dependent approach to robust control for neutral uncertain neural networks with mixed interval time-varying delays

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

This paper considers the problem of delay-dependent global robust stabilization for discrete, distributed and neutral interval time-varying delayed neural networks described by nonlinear delay differential equations of the neutral type. The parameter uncertainties are norm bounded. The activation functions are assumed to be bounded and globally Lipschitz continuous. Using a Lyapunov functional approach and linear matrix inequality (LMI) techniques, the stability criteria for the uncertain neutral neural networks with interval time-varying delays are established in the form of LMIs, which can be readily verified using the standard numerical software. An important feature of the result reported is that all the stability conditions are dependent on the upper and lower bounds of the delays. Another feature of the results lies in that it involves fewer free weighting matrix strategy, and upper bounds of the inner product between two vectors are not introduced to reduce the conservatism of the criteria. Two illustrative examples are provided to demonstrate the effectiveness and the reduced conservatism of the proposed method.

Original languageEnglish
Pages (from-to)1121-1136
Number of pages16
JournalNonlinearity
Volume24
Issue number4
DOIs
Publication statusPublished - 2011 Apr 1

Fingerprint

Interval Time-varying Delay
Delay-dependent
Robust control
Robust Control
Neutral Networks
Neural Networks
Neural networks
intervals
Delayed Neural Networks
Neutral Type
Robust Stabilization
Activation Function
Lyapunov Functional
Stability criteria
Parameter Uncertainty
Delay Differential Equations
Linear matrix inequalities
Stability Criteria
Scalar, inner or dot product
Stability Condition

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

@article{e0e7151f7123404ca2d06157eef646ca,
title = "A delay-dependent approach to robust control for neutral uncertain neural networks with mixed interval time-varying delays",
abstract = "This paper considers the problem of delay-dependent global robust stabilization for discrete, distributed and neutral interval time-varying delayed neural networks described by nonlinear delay differential equations of the neutral type. The parameter uncertainties are norm bounded. The activation functions are assumed to be bounded and globally Lipschitz continuous. Using a Lyapunov functional approach and linear matrix inequality (LMI) techniques, the stability criteria for the uncertain neutral neural networks with interval time-varying delays are established in the form of LMIs, which can be readily verified using the standard numerical software. An important feature of the result reported is that all the stability conditions are dependent on the upper and lower bounds of the delays. Another feature of the results lies in that it involves fewer free weighting matrix strategy, and upper bounds of the inner product between two vectors are not introduced to reduce the conservatism of the criteria. Two illustrative examples are provided to demonstrate the effectiveness and the reduced conservatism of the proposed method.",
author = "Chien-Yu Lu",
year = "2011",
month = "4",
day = "1",
doi = "10.1088/0951-7715/24/4/006",
language = "English",
volume = "24",
pages = "1121--1136",
journal = "Nonlinearity",
issn = "0951-7715",
publisher = "IOP Publishing Ltd.",
number = "4",

}

A delay-dependent approach to robust control for neutral uncertain neural networks with mixed interval time-varying delays. / Lu, Chien-Yu.

In: Nonlinearity, Vol. 24, No. 4, 01.04.2011, p. 1121-1136.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A delay-dependent approach to robust control for neutral uncertain neural networks with mixed interval time-varying delays

AU - Lu, Chien-Yu

PY - 2011/4/1

Y1 - 2011/4/1

N2 - This paper considers the problem of delay-dependent global robust stabilization for discrete, distributed and neutral interval time-varying delayed neural networks described by nonlinear delay differential equations of the neutral type. The parameter uncertainties are norm bounded. The activation functions are assumed to be bounded and globally Lipschitz continuous. Using a Lyapunov functional approach and linear matrix inequality (LMI) techniques, the stability criteria for the uncertain neutral neural networks with interval time-varying delays are established in the form of LMIs, which can be readily verified using the standard numerical software. An important feature of the result reported is that all the stability conditions are dependent on the upper and lower bounds of the delays. Another feature of the results lies in that it involves fewer free weighting matrix strategy, and upper bounds of the inner product between two vectors are not introduced to reduce the conservatism of the criteria. Two illustrative examples are provided to demonstrate the effectiveness and the reduced conservatism of the proposed method.

AB - This paper considers the problem of delay-dependent global robust stabilization for discrete, distributed and neutral interval time-varying delayed neural networks described by nonlinear delay differential equations of the neutral type. The parameter uncertainties are norm bounded. The activation functions are assumed to be bounded and globally Lipschitz continuous. Using a Lyapunov functional approach and linear matrix inequality (LMI) techniques, the stability criteria for the uncertain neutral neural networks with interval time-varying delays are established in the form of LMIs, which can be readily verified using the standard numerical software. An important feature of the result reported is that all the stability conditions are dependent on the upper and lower bounds of the delays. Another feature of the results lies in that it involves fewer free weighting matrix strategy, and upper bounds of the inner product between two vectors are not introduced to reduce the conservatism of the criteria. Two illustrative examples are provided to demonstrate the effectiveness and the reduced conservatism of the proposed method.

UR - http://www.scopus.com/inward/record.url?scp=79952977436&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952977436&partnerID=8YFLogxK

U2 - 10.1088/0951-7715/24/4/006

DO - 10.1088/0951-7715/24/4/006

M3 - Article

VL - 24

SP - 1121

EP - 1136

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 4

ER -