Fractional system identification for lead acid battery state of charge estimation
Signal Processing - Fractional calculus applications in signals and systems
Brief paper: Synthesis of fractional Laguerre basis for system approximation
Automatica (Journal of IFAC)
LMI stability conditions for fractional order systems
Computers & Mathematics with Applications
Brief paper: Analytical computation of the H2-norm of fractional commensurate transfer functions
Automatica (Journal of IFAC)
Synthesis of Complete Orthonormal Fractional Basis Functions With Prescribed Poles
IEEE Transactions on Signal Processing - Part I
Brief paper: Analytical computation of the H2-norm of fractional commensurate transfer functions
Automatica (Journal of IFAC)
Parameter and differentiation order estimation in fractional models
Automatica (Journal of IFAC)
A note on ℒp-norms of fractional systems
Automatica (Journal of IFAC)
Computers & Mathematics with Applications
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Elementary fractional transfer functions are studied in this paper. Some basic properties of elementary transfer functions of the first kind are recalled. Then, two main results are presented regarding elementary fractional transfer functions of the second kind, written in a canonical form and characterized by a commensurate order, a pseudo-damping factor, and a natural frequency. First, stability conditions are established in terms of the pseudo-damping factor and the commensurate order, as a corollary to Matignon's stability theorem. They extend the previous result into conditions that are simpler to check. Then, resonance conditions are established numerically in terms of the commensurate order and the pseudo-damping factor and give interesting information on the frequency behavior of fractional systems. It is shown that elementary transfer functions of the second kind might have up to two resonant frequencies. Moreover, three abaci are given allowing to determine the pseudo-damping factor and the commensurate order for, respectively, a desired normalized gain at each resonance, a desired phase at each resonance, and a desired normalized first or second resonant frequency.