Order reduction via balancing and suboptimal control of a fuel cell – Reformer system

Finding Hankel singular values for singularly perturbed linear continuous‐time systems

“…A proton exchange membrane fuel cell mathematical model has been considered using the balancing transformation in [29]. Its system matrix eigenvalues indicate that this system has three slow and five fast state variables.…”

“…The eigenvalues are given by Since the small singular perturbation parameter is not exactly known, it can be evaluated as the ratio of the fastest eigenvalue of the slow cluster with the slowest eigenvalue of the fast cluster, namely [24, 30]. The system, input, and output matrices are obtained by permuting rows and columns of the original mathematical model matrices from [29] in order to get the explicit singularly perturbed form defined in (15) and (16). The state‐space matrices are given by where …”