Delay-Distribution-Dependent $H_\infty$ State Estimation for Discrete-Time Memristive Neural Networks With Mixed Time-Delays and Fading Measurements

This paper addresses the H
_∞
state estimation issue for a sort of memristive neural networks in the discrete-time setting under randomly occurring mixed time-delays and fading measurements. The main purpose of the addressed issue is to propose a state estimator design algorithm that ensures the error dynamics of the state estimation to be stochastically stable with a prespecified H
_∞
disturbance attenuation index. We put forward certain switching functions to account for the discrete-time yet state-dependent characteristics of the memristive connection weights. By resorting to the robust analysis theory and the Lyapunov-functional analysis theory, we derive some sufficient conditions to guarantee the desired estimation performance. The derived sufficient conditions rely not only on the size of discrete time-delays and the probability distribution law of the distributed time-delays but also on the statistics information of the coefficients of the adopted Rice fading model. Based on the established existence conditions, the gain matrices of the desired estimator are obtained by means of the feasibility of a set of matrix inequalities that can be checked efficiently via available software packages. Finally, the numerical simulation results are provided to show the validity of the main results.