Variance-constrained robust $H_{\mathrm{\infty }}$ state estimation for discrete time-varying uncertain neural networks with uniform quantization

In this paper, we consider the robust $H_{\mathrm{\infty }}$ state estimation (SE) problem for a class of discrete time-varying uncertain neural networks (DTVUNNs) with uniform quantization and time-delay under variance constraints. In order to reflect the actual situation for the dynamic system, the constant time-delay is considered. In addition, the measurement output is first quantized by a uniform quantizer and then transmitted through a communication channel. The main purpose is to design a time-varying finite-horizon state estimator such that, for both the uniform quantization and time-delay, some sufficient criteria are obtained for the estimation error (EE) system to satisfy the error variance boundedness and the $H_{\mathrm{\infty }}$ performance constraint. With the help of stochastic analysis technique, a new $H_{\mathrm{\infty }}$ SE algorithm without resorting the augmentation method is proposed for DTVUNNs with uniform quantization. Finally, a simulation example is given to illustrate the feasibility and validity of the proposed variance-constrained robust $H_{\mathrm{\infty }}$ SE method.