A novel noise-tolerant Zhang neural network for time-varying Lyapunov equation

• Main Authors: Min Sun, Jing Liu
• Format: Article
• Language: English
• Published: SpringerOpen 2020-03-01
• Series: Advances in Difference Equations
• Subjects: Time-varying Lyapunov equation; Noise-tolerant continuous-time Zhang neural network; Noise-tolerant discrete-time Zhang neural network; Global convergence
• Online Access: http://link.springer.com/article/10.1186/s13662-020-02571-7

Abstract The Zhang neural network (ZNN) has become a benchmark solver for various time-varying problems solving. In this paper, leveraging a novel design formula, a noise-tolerant continuous-time ZNN (NTCTZNN) model is deliberately developed and analyzed for a time-varying Lyapunov equation, which inherits the exponential convergence rate of the classical CTZNN in a noiseless environment. Theoretical results show that for a time-varying Lyapunov equation with constant noise or time-varying linear noise, the proposed NTCTZNN model is convergent, no matter how large the noise is. For a time-varying Lyapunov equation with quadratic noise, the proposed NTCTZNN model converges to a constant which is reciprocal to the design parameter. These results indicate that the proposed NTCTZNN model has a stronger anti-noise capability than the traditional CTZNN. Beyond that, for potential digital hardware realization, the discrete-time version of the NTCTZNN model (NTDTZNN) is proposed on the basis of the Euler forward difference. Lastly, the efficacy and accuracy of the proposed NTCTZNN and NTDTZNN models are illustrated by some numerical examples.