A new type of recurrent neural networks for real-time solution of Lyapunov equation with time-varying coefficient matrices

Abstract

A new kind of recurrent neural network is presented for solving the Lyapunov equation with time-varying coefficient matrices. Different from other neural-computation approaches, the neural network is developed by following Zhang et al.'s design method, which is capable of solving the time-varying Lyapunov equation. The resultant Zhang neural network (ZNN) with implicit dynamics could globally exponentially converge to the exact time-varying solution of such a Lyapunov equation. Computer-simulation results substantiate that the proposed recurrent neural network could achieve much superior performance on solving the Lyapunov equation with time-varying coefficient matrices, as compared to conventional gradient-based neural networks (GNN).