state estimation for discrete-time memristive recurrent neural networks with stochastic time-delays

Abstract

This paper deals with the robust $H_{\infty }$ state estimation problem for a class of memristive recurrent neural networks with stochastic time-delays. The stochastic time-delays under consideration are governed by a Bernoulli-distributed stochastic sequence. The purpose of the addressed problem is to design the robust state estimator such that the dynamics of the estimation error is exponentially stable in the mean square, and the prescribed $H_{\infty }$ performance constraint is met. By utilizing the difference inclusion theory and choosing a proper Lyapunov–Krasovskii functional, the existence condition of the desired estimator is derived. Based on it, the explicit expression of the estimator gain is given in terms of the solution to a linear matrix inequality. Finally, a numerical example is employed to demonstrate the effectiveness and applicability of the proposed estimation approach.

Keywords:

• Discrete time
• $H_{\infty }$ state estimation
• memristive neural networks
• stochastic time-delays

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [grant number 61329301], [grant number 61134009], [grant number 61473076], [grant number 61503001]; the Shu Guang project of Shanghai Municipal Education Commission and Shanghai Education Development Foundation [grant number 13SG34]; the Natural Science Foundation of Universities in Anhui Province [grant number KJ2015A088], [grant number TSKJ2015B17]; the Fundamental Research Funds for the Central Universities, the DHU Distinguished Young Professor Program, and the Alexander von Humboldt Foundation of Germany.