State-Feedback Filtering for Delayed Discrete-Time Complex-Valued Neural Networks

This article explores a new filtering problem for the class of delayed discrete-time complex-valued neural networks (CVNNs) via state-feedback control design. The novelty of this article comes from the consideration of the newly developed complex-valued reciprocal convex matrix inequality as well as the complex-valued Jensen-based summation inequalities (JSIs). By employing an appropriate Lyapunov-Krasovskii functional (LKF) and by using newly proposed complex-valued inequalities, attention is concentrated on the design of a state-feedback filter such that the associated filtering error system is asymptotically stable with prescribed filter and control gain matrices. The proposed theoretical results are presented in terms of complex-valued linear matrix inequalities (LMIs) that can be solved numerically by using the YALMIP toolbox in MATLAB software. Additionally, one numerical example is given to confirm the validity of the resulting sufficient conditions with the availability of the suitable control and filter design.