Time-invariant Lyapunov matrix equation solving by Neural Networks with Simulink models

This paper mainly focuses on solving problem of time-invariant Lyapunov matrix equation via Zhang neural network and traditional gradient-based neural network. Generally speaking, based on constructing an unbounded error function, Zhang Neural Networks (ZNN) is depicted in an explicit dynamics for time-varying matrix equation solving, while the traditional Gradient-based Neural Networks (GNN) is an implicit dynamics by defining a scalar-valued norm-based energy function only for the time-invariant matrix problem solving. By using the Simulink software package, Simulink dynamic models could be constructed for these two neural networks in this paper, separately. An illustrative simulation results show that these two type of neural networks could both be used to solve such matrix equation efficiently. Moreover, the ZNN may get superior convergent performance and higher precision than GNN.