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Different-level dynamic linear system (DLDLS) is an interesting and challenging topic due to its complicated structure and time-variant characteristic. To solve this difficult problem, the equivalency of solutions at different levels is analyzed and obtained via zeroing neural network (ZNN) method. Based on the equivalency, a continuous ZNN model is proposed to solve the continuous DLDLS. For easier hardware realization, a new Zhang et al. discretization formula with high precision is proposed for the continuous ZNN model discretization, and the corresponding new discrete ZNN (NDZNN) model is proposed to solve discrete DLDLS. Note that the NDZNN model satisfies the requirement of real-time computation because it has the online ability to predict the solution for the future instant. Furthermore, the problems of robot manipulator control with additional restrictions (e.g., joint damage) are formulated as specific discrete DLDLS, and the proposed NDZNN model is employed to solve such problems. Simulation results substantiate the effectiveness of NDZNN model. [ABSTRACT FROM AUTHOR]