A Finite-Time Convergent Neurodynamic Model for Complex-Valued Time-Varying Matrix Inversion Based on Symmetric Norm Operator

Complex-valued time-varying matrix inversion (CTMI) plays a crucial role in many engineering and scientific applications, yet achieving fast and robust solutions while maintaining a simple structure is a challenging task. In this paper, a novel finite-time convergent neurodynamic model (FTCN) is proposed for solving CTMI problems efficiently. Distinct from existing approaches, the FTCN model is developed based on the symmetric operator Frobenius norm, which enables a simplified structure without relying on complicated activation functions or integral terms. Rigorous theoretical analysis is conducted to establish the finite-time convergence of the proposed model under both noise-free and bounded noise conditions. To validate the effectiveness of the proposed FTCN model, comprehensive numerical simulations are performed. The experimental results confirm the global convergence property of the FTCN model and its capability in handling large-dimensional CTMI problems. Furthermore, comparisons with existing models under noisy environments demonstrate the superior performance of the proposed FTCN model.