Optimal model simplification for systems having delays in inputs, outputs and states

A recently proposed method for the simplification of single variable systems having ordinary polynomial denominators has been extended to the multivariable case encompassing situations where the original or simplified model may have delays in their states. The performance index used for optimization is the integral of the time-weighted squared error between the responses of the original and simplified models. The performance index is first expressed in terms of the simplified model unknown parameters and a minimization of this index gives the simplified model optimal parameters. The results of this work find additional application in obtaining the closed-form expressions of the error squared integral between the reference input and output response for certain closed-loop systems involving plants with time delays.