Noise-Tolerant Zeroing Neural Network for Solving Non-Stationary Lyapunov Equation

As a crucial means for stability analysis in control systems, the Lyapunov equation is applied in many fields of science and engineering. There are some methods proposed and studied for solving the non-stationary Lyapunov equation, such as the zeroing neural network (ZNN) model. However, a common drawback these methods have is that they rarely tolerate noises. Therefore, given that the existence of various types of noises during computation, a noise-tolerant ZNN (NTZNN) model with anti-noise ability is proposed for solving the non-stationary Lyapunov equation in this paper. For comparison, the conventional ZNN (CZNN) model is also applied to solve the same problem. Furthermore, theoretical analyses are provided to prove the global and exponential convergence performance of the proposed NTZNN model in the absence of noises. On this basis, the anti-noise performance of the proposed NTZNN model is proven. Finally, by adopting the proposed NTZNN model and the CZNN model to solve the non-stationary Lyapunov equation, computer simulations are conducted under the noise-free case and the noisy case, respectively. The simulation results indicate that the proposed NTZNN model is practicable for solving the non-stationary Lyapunov equation and superior to the CZNN model at the existence of noises.