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

Luo, Jiajie; Li, Jichun; Holderbaum, William; Li, Jiguang

Abstract

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 FPZNN 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.

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 2024 IEEE International Conference on Cybernetics and Intelligent Systems (CIS) and IEEE International Conference on Robotics, Automation and Mechatronics (RAM)
• Start Date: Aug 8, 2024
• End Date: Aug 11, 2024
• Acceptance Date: Jun 1, 2024
• Online Publication Date: Sep 16, 2024
• Publication Date: Aug 11, 2024
• Deposit Date: Nov 1, 2024
• Publisher: Institute of Electrical and Electronics Engineers
• Pages: 543-548
• Book Title: 2024 IEEE International Conference on Cybernetics and Intelligent Systems (CIS) and IEEE International Conference on Robotics, Automation and Mechatronics (RAM)
• ISBN: 9798350364200
• DOI: https://doi.org/10.1109/cis-ram61939.2024.10672985