Optimal model reduction for systems with time delay

This paper deals with the problem of optimally approximating high order models with or without time delay by low order ones with or without time delay. The performance index used for optimization is the integral squared error (ISE) between the responses of the reduced order and original models. The ISE is first expressed in terms of the reduced order system unknown parameters and a minimization of the ISE then gives the reduced model optimal parameters. Cheap computation of optimal reduced order models with time delay has hitherto proved abortive as closed-form expressions for the ISE has proved difficult to obtain.