Distributed functional fractional‐order state observers using sampled measurements for nonlinear fractional‐order interconnected systems

In this paper, a new distributed functional fractional‐order state observer design method is proposed for nonlinear fractional‐order interconnected systems subject to external disturbances. Unlike the traditional distributed functional state observers, which are used for a minimal sampling period, the one in this paper uses sampled output measurements, which may be useful in the presence of “medium‐size” sampling periods. The structures of the functional fractional‐order state observer with sampled measurement for each subsystem are first proposed, and then based on some algebraic transformations inequalities, including the Cauchy matrix inequality and the Schur complement lemma existence conditions, an existence condition of the proposed distributed state observer is established and formulated in terms of a convex optimization problem. Finally, a numerical example with simulation results is provided to illustrate the feasibility of the proposed theories.