Truncation criteria for model reduction using balanced realisation

It is shown with an example that the reduction technique using balanced realisation suggested previous (Moore 1981) may not retain the most significant states. An example is presented which shows that there are cases where the truncation of states using the second-order modes instead of d_i (products of the second-order modes and the input or output vector of the balanced realisation) leads to better approximation of the impulse response