Feedback is ubiquitous in gene regulatory networks, and provide e.g. homeostasis and signal amplification. The presence of feedback has significant implications for network inference since it implies that the gene responses to perturbation experiments typically will be strongly correlated, leading to ill-conditioning of the measurement matrix. The ill-conditioning will represent a fundamental problem in network identification since it implies that some of the network interactions will be identified with gross errors. This problem is in Bioinformatics commonly dealt with by using principal component analysis or clustering to reduce the dimension of the state space. Reduction of the dimension, however, gives a network interaction graph that may be very different from the true system. We therefore propose a fundamentally different approach to overcome this problem, namely a systematic iterative experiment design that ensures sufficient excitations of all network interactions. A method that leads to combinatorial perturbation experiments, in which a number of genes are perturbed simultaneously.