Neural Computing and Applications

, Volume 24, Issue 7–8, pp 1639–1645 | Cite as

Observer-based control for time-varying delay neural networks with nonlinear observation

  • V. N. PhatEmail author
  • T. Fernando
  • H. Trinh
Original Article


This paper studies the problem of designing observer-based controllers for a class of delayed neural networks with nonlinear observation. The system under consideration is subject to nonlinear observation and an interval time-varying delay. The nonlinear observation output is any nonlinear Lipschitzian function and the time-varying delay is not required to be differentiable nor its lower bound be zero. By constructing a set of appropriate Lyapunov–Krasovskii functionals and utilizing the Newton–Leibniz formula, some delay-dependent stabilizability conditions which are expressed in terms of Linear Matrix Inequalities (LMIs) are derived. The derived conditions allow simultaneous computation of two bounds that characterize the exponential stability rate of the closed-loop system. The unknown observer gain and the state feedback observer-based controller are directly obtained upon the feasibility of the derived LMIs stabilizability conditions. A simulation example is presented to verify the effectiveness of the proposed result.


Neural networks Observer-based control Nonlinear observation Interval time-varying delay Linear matrix inequalities Lyapunov–Krasovskii functionals 



This work was supported by the Australian Research Council under the Discovery grant DP130101532 and the National Foundation for Science and Technology Development, Vietnam, grant number 101.01-2011.51.


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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.Institute of Mathematics, VASTHanoiVietnam
  2. 2.School of Electrical, Electronic and Computer Engineering, University of Western AustraliaPerthAustralia
  3. 3.School of EngineeringDeakin UniversityGeelongAustralia

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