Multi-step ahead predictions for multivariable linear stochastic systems via model recursion

The multi-step ahead prediction method for the output of a multivariable linear discrete-time stochastic system, directly based on the recrusion of system model, is developed. The basic procedures are: 1) rewrite the original system model into an one-step ahead recursive version; 2) repeatly use this recursion step by step and thus successively gain all the needed multi-step ahead predictions. It is proved that this model recursion method is strictly equivalent to the existing method using the recursion of multivariable Dio-phantine equation, under the condition of white noise. The proposed method possesses advantages both in computational reduction and programming simplicity, and has successfully been used in multivariable modified generalized predictive controller.