Multivariable Smith Predictors design for nonsquare plants

The goal of this brief is to provide a solution to the optimal design problem of decoupled multivariable Smith Predictor for general linear stable plants with multiple time delays. The design procedure is divided into three steps. In the first step, a non-square plant is factored into the "delay free" part and delay part, and the "delay free" part is further factored into minimum phase part and nonminimum phase part. In the second step, the factorization is utilized to analytically derive the optimal multivariable Smith Predictor based on only output feedback. Finally, the controller is shaped by a filter for specified inputs and a simple procedure is developed to quantitatively tune the closed-loop response expressed in time domain or frequency domain.