Stability analysis of multivariable predictive control - a polynomial approach

A rigorous method for analyzing the stability and performance of unconstrained multivariable predictive controllers is developed using polynomial operators and coprime matrix factorizations. The stability of the closed-loop systems is assessed in terms of two characteristic equations that define the system poles. It is also shown that a closed-loop stable predictive controller delivers offset free tracking for a set of plants satisfying specific conditions. The large number of prediction and control horizons that can be specified complicates the tuning of predictive controllers; however, the task is facilitated with the aid of the tools presented here because unstable horizon selections can be identified and rejected. The analysis approach is illustrated with an example.