A New General Fast Neurodynamics (GFN) for Solving Complex Generalized Sylvester Equation With Power Systems Application

ABSTRACT The study on topics related to solving matrix equations with complex coefficients initiates an interesting topic for research in the previous decades. In this research document, a novel and general‐fast recurrent neural network (RNN) model, based on an extended activation function (AF), will be designed for solving the generalized Sylvester equation with complex coefficients. The key innovation of the new extended activation function, compared to existing functions, is based on a set of constants in the new AF which reduces the fixed convergence time of the corresponding general‐fast RNN formula. Convergence analysis and numerical experiments in Simulink will show the efficiency and the accelerated convergence ability of the proposed dynamical system. Furthermore, the novel neurodynamics is applied for the control of a single‐machine bus model and for computing the different currents in electrical circuits.