Loose Error Bounds and Exponential Convergence Rates of GMDS-ZNN for Time-Dependent Inverse Computing

Time-dependent matrix processing, especially the time-dependent inverse computing, plays an important role in mathematics science, control and industrial electronics fields. On the basis of previous work, Getz-Marsden dynamic system-Zhang neural network (GMDS-ZNN, or simply, GZ neurodynamics, GZND) has been shown as an effective neurodynamics method for the time-dependent inverse computing. In this paper, we analyze the stability and error properties of two GMDS-ZNN models for the time-dependent inverse computing by Lyapunov stability theory. As results, we present four theorems that describe the loose error bounds and exponential convergence rates of two GMDS-ZNN models for the time-dependent inverse computing. Moreover, we present two corollaries that describe the properties of the unit balls of the corresponding residual errors as well as solution errors of GMDS-ZNN models, which may be useful for proving the zero vanishing of solution errors in the future.