State-Space Neural Network with Ordered Variance

This paper presents a novel state-space neural network with ordered variance (SSNNO) in which the state variables are ordered in decreasing variance. A systematic way of identifying the order of the model with SSNNO is proposed, which is further extended for model order reduction. Theoretical results on the existence of SSNNO with an arbitrarily small prediction error is presented. The effectiveness of the SSNNO in system identification and model order reduction is illustrated using simulation results.