An Empirical Method for Approximate H-2 Optimal Model Order Reduction

In this paper, we discuss an empirical method of finding a reduced order H-2 optimal model for a single input single output (SISO) linear time-invariant (LTI) system. We see the impulse distribution as a limit point of a sequence of Gaussian signals. We find a sequence of reduced order models that approximate the system's response to a sequence of Gaussian signals with decreasing standard deviation. We show that the limit point of this sequence of models is the reduced order H-2 optimal model.