Robust Adaptive Control for Fractional-Order Systems with Disturbance and Saturation

Appendix C

Laplace Transforms Involving Fractional Operations

Like integer-order systems, the Laplace transform and its inversion are very important. In this appendix, the Laplace transform definition is given first. Then some essential special functions are described. Finally, tables of inversions of Laplace transforms involving fractional and irrational-order operators are given [243].

C.1 Laplace Transforms

For a time-domain function , its Laplace transform in the -domain is defined as

C.1

where is the notation of Laplace transform.

If the Laplace transform of a signal is , the inverse Laplace transform of is defined as

C.2

where is greater than the real part of all the poles of ...