On model reduction by L2-optimal pole retention

Abstract The L 2 -optimal reduced model retaining a given number of poles of the original system is determined in an efficient way. In particular, an expression for evaluating the minimum of the impulse response error norm for any choice of retained poles is derived in terms of the original system parameters, which allows us to find the truly dominant poles in a simple manner. Then, the corresponding optimal model numerator is obtained using an order- recursive procedure. An interesting interpolation property of the reduced model is also pointed out. An example shows how the method operates.