The pointwise completeness and pointwise degeneracy of standard and positive fractional linear discrete-time and continuous-time systems with state-feedbacks are addressed. It is shown that the pointwise completeness and pointwise degeneracy of the fractional positive continuous-time systems are invariant under the state and output feedbacks. Necessary and sufficient conditions are established for the existence of gain matrices of state-feedbacks for standard and positive linear systems such that the closed-loop systems are pointwise complete. Considerations are illustrated by numerical examples.
Responses of positive standard and fractional continuous-time and discrete-time linear systems with derivatives of their inputs are presented herein. It is shown that the formulae for state vectors and outputs are also valid for their derivatives if the inputs and outputs and their derivatives of suitable order are zero for t = 0. Similar results are also shown for positive standard and fractional discrete-time linear systems.