Bounded Z-type neurodynamics with limited-time convergence and noise tolerance for calculating time-dependent Lyapunov equation

Z-type neurodynamics (ZND) is an effective tool for calculating time-dependent problems and has been extensively used. However, the convergence rate and the noise tolerance of ZND models have frequently been addressed separately. In this work, a unified design formula for the ZND is proposed by combining the nonlinear activation function and the integral term. On the basis of a formula, a bounded ZND (BZND) model is proposed and used to compute a real-time-dependent Lyapunov equation in noisy environments. Notably, the proposed BZND model, which adopts the Li activation function, not only converges in a limited time but also has inherently noise-tolerant characteristics. Theoretical analyses of the convergence and robustness of the BZND model are further presented. In addition, the upper bound of convergence time is also derived theoretically. Finally, illustrative examples are conducted. Results confirm the superior performance of the proposed BZND model for calculating the real-time-dependent Lyapunov equation with various types of noise to the existing ZND models.