Fractional-order Hammerstein state-space modeling of nonlinear dynamic systems from input-output measurements.

This paper introduces a continuous-time fractional-order Hammerstein state-space model with a systematic identification algorithm for modeling nonlinear dynamic systems. The proposed model consists of a radial-basis function neural network followed by a fractional-order system. The proposed identification scheme is accomplished in two stages. The structural parameters of the fractional-order system (i.e. the values of the fractional order and the degree of the denominator in the fractional-order system) are estimated in the frequency domain. Then, the synaptic weights of the radial-basis function neural network and the coefficients of the fractional-order system are determined in the time domain via the Lyapunov stability theory, which guarantees stability of the given method and its convergence under a mild condition. Three examples are provided to show the effectiveness of the proposed method.