Comparison on neural solvers for the Lyapunov matrix equation with stationary & nonstationary coefficients

Abstract In this paper, two types of recurrent neural network (RNN) are comparatively developed and exploited for the online solution of the well-known Lyapunov matrix equation with the stationary and nonstationary coefficients. Based on a new design method, the resultant Zhang neural networks (ZNN) are generalized and presented to solve the stationary and nonstationary problems with accuracy and efficiency. For comparison, the conventional gradient-based neural networks (GNN) are also used for the same problems. Computer simulation results show that, when used to solve the whether stationary or nonstationary problems, the convergence performance of ZNN solvers are superior than that of GNN solvers.