Recurrent neural networks for solving linear matrix equations

Recurrent neural networks for solving linear matrix equations are proposed. The proposed recurrent neural networks consist of two bidirectionally connected layers and each layer consists of an array of neurons. The proposed recurrent neural networks are shown to be asymptotically stable in the large and capable of computing inverse matrices and solving Lyapunov matrix equations. The operating characteristics of the proposed recurrent neural networks are demonstrated via several illustrative examples.