Trapezoidal rule for numerical evaluation of fractional order integrals with applications to simulation and identification of fractional order systems

This paper presents an extension of the well-known trapezoidal (bilinear) integration rule, that in the present work is applied to the numerical evaluation of fractional-order integrals. Particularly, this approximation is exploited to derive viable numerical algorithms addressing two distinct problems: i) simulation of Linear Time-Invariant (LTI) Commensurate Fractional Order Systems (CFOS); ii) non-recursive parameter estimation in LTI-CFOS. More precisely, the problem of non-recursive parameter estimation is addressed in two different scenarios. The first one is when the commensurate order of the CFOS is known in advance, while the second, more general, one is that in which the commensurate order is unknown and is to be estimated. The effectiveness of the proposed methods is illustrated by numerical examples.