Mapping error of linear dynamic systems caused by reduced-order model

This paper presents a theory and its practical application for the determination of the mapping error of the linear time invariant dynamic system by a simplified model. This mapping is expressed by means of the integral-square-error criterion. A special calculation algorithm showing how to compute the maximum value of this criterion is discussed and presented in detail. This paper also shows a method of a synthesis of a special class of simplified models, which near the beginning of the time interval, map the models of a higher order with the error approaching zero. The particular transformations, presented in a matrix notation, are defined. The theory presented is illustrated with a numerical example.