Least squares reduction of linear systems using impulse response

Abstract

Necessary conditions for the optimum linear dynamic model reduction problem subject to a pulse input (Dirac delta function) are derived. These conditions are based on the integral square error and are applicable to multiple input-single output systems. Such a problem can be made computationally feasible for finite and infinite time intervals and for various forms of the low order system. A numerical example based on unsteady state heat conduction is presented