Non Integer Model from Modal Decomposition for Time Domain System Identification

By O. Cois, Alain Oustaloup, E. Battaglia, J. Battaglia. 2000

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TUTORIAL ON SYSTEM IDENTIFICATION USING FRACTIONAL DIFFERENTIATION MODELS (2006, background): “The idea of optimizing the commensurate order instead of all differentiation orders was first introduced in (Cois et al., 2000) who chose to write the transfer function (13) in a modal form as in (7).”
Subspace identification for fractional order Hammerstein systems based on instrumental variables (2012, methodology): “In [6,7], modal fractional models based on the diagonal representation form were skillfully used and the parameters to-be-identified were transformed into modal parameters.”
Fractional system identification for lead acid battery state of charge estimation (2006, methodology): “In system identification field, several methods were created [8,9] that permit to take into account systems with long memory phenomenon (or diffusion phenomenon).”
Fractional Kalman filter algorithm for the states, parameters and order of fractional system estimation (2006, background): “Keywords: discrete fractional state-space systems, fractional Kalman filter, parameters estimation, order estimation, extended fractional Kalman filter”
An overview of the CRONE approach in system analysis, modeling and identification, observation and control (2008, background): “Studies on real systems such as thermal or electrochemical (Battaglia et al., 2000, Cois et al., 2000), reveal fractional behavior.”