On the initial conditions in continuous-time fractional linear systems

Authors:
Manuel Duarte Ortigueira
Affiliations:
UNINOVA/DEE, Faculdade de Ciências e Tecnologia da UNL, Campus da FCT da UNL, Quinta da Torre, 2829-516 Caparica, Portugal and INESC, R. Alves Redol, 9, 1000-029 Lisboa, Portugal
Venue:
Signal Processing - Special issue: Fractional signal processing and applications
Year:
2003

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Abstract

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.