document: Dynamics and control of initialized fractional-order systems Due to the importance of historical effects in fractional-order systems , this paper presents a general fractional-order system and control theory that includes the time-varying initialization response . Previous studies have not properly accounted for these historical effects . The initialization response , along with the forced response , for fractional-order systems is determined . The scalar fractional-order impulse response is determined , and is a generalization of the exponential function . Stability properties of fractional-order systems are presented in the complex w-plane , which is a transformation of the s-plane . Time responses are discussed with respect to pole positions in the complex w-plane and frequency response behavior is included . A fractional-order vector space representation , which is a generalization of the state space concept , is presented including the initialization response . Control methods for vector representations of initialized fractional-order systems are shown . Finally , the fractional-order differintegral is generalized to continuous order-distributions which have the possibility of including all fractional orders in a transfer function
doc_bio_tags: B O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B I O O O O O O O O O O O O O B I O O O O B I O O O O O O O O O O B I O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O B I I O O O O O B I O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I
extractive_keyphrases: dynamics control initialization response forced response impulse response exponential function vector space representation state space concept transfer function
abstractive_keyphrases: initialized fractional-order systems fractional-order differintegral