Nonlinear Dynamics

, Volume 94, Issue 2, pp 1215–1225 | Cite as

State estimation of fractional-order delayed memristive neural networks

  • Haibo Bao
  • Jinde CaoEmail author
  • Jürgen Kurths
Original Paper


This paper focuses on designing state estimators for fractional-order memristive neural networks (FMNNs) with time delays. It is meaningful to propose a suitable state estimator for FMNNs because of the following two reasons: (1) different initial conditions of memristive neural networks (MNNs) may cause parameter mismatch; (2) state estimation approaches and theories for integer-order neural networks cannot be directly extended and used to deal with fractional-order neural networks. The present paper first investigates state estimation problem for FMNNs. By means of Lyapunov functionals and fractional-order Lyapunov methods, sufficient conditions are built to ensure that the estimation error system is asymptotically stable, which are readily solved by MATLAB LMI Toolbox. Ultimately, two examples are presented to show the effectiveness of the proposed theorems.


State estimation Fractional-order Memristive neural networks Time delay 



This work was jointly supported by the National Natural Science Foundation of China under Grant Nos. 61573291 and 61573096, the Grant of China Scholarship Council 201408505020, the Fundamental Research Funds for Central Universities XDJK2016B036, the Jiangsu Provincial Key Laboratory of Networked Collective Intelligence under Grant No. BM2017002.

Compliance with ethical standards

Conflicts of interest

The authors declare that there is no conflict of interest.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsSouthwest UniversityChongqingChina
  2. 2.Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, School of MathematicsSoutheast UniversityNanjingChina
  3. 3.School of Electrical EngineeringNantong UniversityNantongChina
  4. 4.School of Mathematics and StatisticsShandong Normal UniversityJinanChina
  5. 5.Institute of PhysicsHumboldt University of BerlinBerlinGermany
  6. 6.Potsdam Institute for Climate Impact ResearchPotsdamGermany

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