On the initial conditions in continuous-time fractional linear systems. (English) Zbl 1145.94367

Summary: The initial condition problem for fractional linear system initialisation is studied in this paper. It is based on the generalised initial value theorem. The new approach involves functions belonging to the space of Laplace transformable distributions verifying the Watson-Doetsch lemma. The fractional derivatives of these functions are independent of the derivative definition. This class includes the most important functions appearing in computing the Impulse Response of continuous-time fractional linear systems.


94A12 Signal theory (characterization, reconstruction, filtering, etc.)
26A33 Fractional derivatives and integrals
93E12 Identification in stochastic control theory
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