  Fractional-order dynamical networks are increasingly being used to model and
describe processes demonstrating long-term memory or complex interlaced
dependencies amongst the spatial and temporal components of a wide variety of
dynamical networks. Notable examples include networked control systems or
neurophysiological networks which are created using electroencephalographic
(EEG) or blood-oxygen-level-dependent (BOLD) data. As a result, the estimation
of the states of fractional-order dynamical networks poses an important
problem. To this effect, this paper addresses the problem of minimum-energy
state estimation for discrete-time fractional-order dynamical networks
(DT-FODN), where the state and output equations are affected by an additive
noise that is considered to be deterministic, bounded, and unknown.
Specifically, we derive the corresponding estimator and show that the resulting
estimation error is exponentially input-to-state stable with respect to the
disturbances and to a signal that is decreasing with the increase of the
accuracy of the adopted approximation model. An illustrative example shows the
effectiveness of the proposed method on real-world neurophysiological networks.
