$$H_{\infty }$$ H ∞ state estimation for discrete-time stochastic memristive BAM neural networks with mixed time-delays

Abstract

In this paper, the $$H_\infty$$ state estimation problem is investigated for a class of discrete-time stochastic memristive bidirectional associative memory (DSMBAM) neural networks with mixed time delays. The mixed time delays comprise both discrete and distributed time-delays. A series of novel switching functions are proposed to reflect the state-dependent characteristics of the memristive connection weights in the discrete-time setting, which facilitates the dynamics analysis of the addressed memristive neural networks (MNNs). By means of the introduced series of switching functions, an $$H_\infty$$ state estimator is designed such that the estimation error is exponentially mean-square stable and the prescribed $$H_\infty$$ performance requirement is achieved. The gain matrices of the desired estimator are parameterized by utilizing the semi-definite programming method. Finally, a simulation example is employed to demonstrate the usefulness and effectiveness of the proposed theoretical results.