A Novel Approach for Solving the Time-Varying Complex-Valued Linear Matrix Inequality Based on Fuzzy-Parameter Zeroing Neural Network

Solving linear matrix inequality (LMI) is crucial across diverse fields, and the emergence of zeroing neural networks (ZNN) presents a novel solution for the time-varying LMI (TV-LMI) challenge. However, the application of ZNN to solve the time-varying complex-valued LMI (TVCV-LMI) problem remains unexplored. Therefore, we introduce a novel fuzzy-parameter ZNN (FP-ZNN) model in this study to tackle the TVCV-LMI problem. With the introduction of fuzzy logic system (FLS), the FP-ZNN model is able to adjust the fuzzy convergence parameter (FCP) in a real-time manner, responding to any change in the system error and achieving the best performance. We also use an exponential activation function (EAF) in our study, which makes the FP-ZNN model fixed-time stable. To verify and illustrate the superior features of the elegant FP-ZNN model, detailed theoretical analysis, together with numerical experiments, are provided, and the results emphasize the fixed-time stability and adaptiveness of the FP-ZNN model further. As a novel approach, we provide an elegant solution to the TVCV-LMI problem in this paper.