State estimation of fractional-order delayed memristive neural networks

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.