Set inversion via interval analysis for nonlinear bounded-error estimation
Automatica (Journal of IFAC) - Special section on fault detection, supervision and safety for technical processes
Fractional system identification for lead acid battery state of charge estimation
Signal Processing - Fractional calculus applications in signals and systems
Artificial Intelligence
Automatica (Journal of IFAC)
LMI stability conditions for fractional order systems
Computers & Mathematics with Applications
Brief paper: Interval observer design for consistency checks of nonlinear continuous-time systems
Automatica (Journal of IFAC)
Brief paper: Stability and resonance conditions of elementary fractional transfer functions
Automatica (Journal of IFAC)
Parameter and differentiation order estimation in fractional models
Automatica (Journal of IFAC)
Fractional models for modeling complex linear systems under poor frequency resolution measurements
Digital Signal Processing
Computers & Mathematics with Applications
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In this paper, the usual definition of Grunwald-Letnikov fractional derivative is first extended to interval derivatives in order to deal with uncertainties in the differentiation orders. The Laplace transform of interval derivatives is computed and its monotonicity is studied in the frequency domain. Next, the main objectives of this paper are presented as the implementation of three methods for set membership parameters estimation of fractional differentiation models based on complex frequency data. The first one uses a rectangular inclusion function with rectangle sides corresponding to real and imaginary parts of the complex frequency response; the second one uses a polar inclusion function and the gain/phase representation; the third one uses a circular inclusion function with disk representation. Each inclusion function introduces pessimism differently. It is shown that all three approaches are complementary and that the results can be merged to obtain a smaller feasible solution set. The proposed methods can be applied to estimate parameters of certain/uncertain linear time variant/invariant systems.