Identification of linear systems with time delay and unknown order

This paper proposes a system identification method for linear systems with time delay and unknown order. We hypothesize a number of candidate models, which have different order, because system order is unknown. In each model, we estimate the model parameters based on the maximum likelihood method by using nonlinear optimization technique. Then both local optimization technique and global search method are used because the estimated parameters may fall into a local minimum. After all candidate model's parameters are estimated, one model is selected among these models to estimate the system order by using a posteriori probability based on Bayes's theorem. Finally, the validity of the proposed method is demonstrated by numerical examples. (C) 2003 Wiley Periodicals, Inc.