Predefined-Time Stability-Based Zeroing Neural Networks and Their Application in Solving the Lyapunov Equation

Lyapunov equation is extensively applied in engineering areas, and zeroing neural networks (ZNN) are very effective in solving this kind of equation. In this paper, two predefined-time stability theorems are used to devise new activation functions. Then, we obtain two new ZNN models, which are applied in solving the Lyapunov equation. This type of model is called the predefined-time stability-based zeroing neural network model. Compared with the ZNN models which have existed, the proposed model retains the noise-tolerant virtue and gains a new advantage: predefined-time convergence. Lastly, we verify that the model developed in this paper is superior to the known models in solving the time-variant Lyapunov equation via numerical simulations.