Peng-Type ZNN Model Attempted for Online Diagonalization of Time-Varying Symmetric Matrix

Matrix diagonalization (or termed, matrix eigen-decomposition) is a vital part of matrix theory. Different from static matrix diagonalization problem, in this paper, the more challenging problem, i.e., time-varying symmetric matrix diagonalization problem, is mainly researched. For solving this problem, the ZNN (i.e., Zhang neural network) design method is employed, which has been formally proposed for finding online solutions of various time-varying problems. Besides, the try-and-error method is adopted to simplify an intermediate model. Then, an effective model termed Peng-type ZNN model is proposed and discussed. In order to verify the validity of the proposed model, three examples are considered. Simulation results illustrate that the steady-state errors are limited to a relatively small level, and the steady-state errors can be controlled by changing the diagonal matrix in the model. Therefore, the effectiveness of the proposed Peng-type ZNN model is testified.