id: 05830268
dt: j
an: 05830268
au: Trigeassou, J.C.; Maamri, N.
ti: Initial conditions and initialization of linear fractional differential
    equations.
so: Signal Process. 91, No. 3, 427-436 (2011).
py: 2011
pu: Elsevier Science, Amsterdam
la: EN
cc: 
ut: fractional order differential equation; initial conditions; fractional
    integrator; state space representation; observer
ci: 
li: doi:10.1016/j.sigpro.2010.03.010
ab: Summary: Mastery of the initial conditions of fractional order systems
    remains an open problem, in spite of a great number of contributions.
    This paper proposes a solution dedicated to linear fractional
    differential equations (FDEs), which is based on an equivalence
    principle between the original system and an exactly equivalent
    infinite dimensional ordinary differential equation (ODE). This
    equivalence principle is derived from the fractional integration
    operator concept and the frequency distributed state space model of
    this operator. Thanks to this principle, the FDE initial conditions
    problem is converted into a conventional ODE initialization problem,
    however with an infinite dimensional state vector. Practical FDE
    initialization is performed using an observer based technique applied
    to the equivalent ODE; a numerical example demonstrates the efficiency
    of this approach.
rv: