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