Abstract
The solution to the system of equations of the descriptor linear discrete-time with different fractional orders is derived by the use of the Drazin inverse of matrices. This solution is applied to analysis of the pointwise completeness and the pointwise degeneracy of the descriptor discrete-time linear systems with different fractional orders. Necessary and sufficient conditions for the pointwise completeness and the pointwise degeneracy of the descriptor discrete–time linear systems with different fractional orders are established. The proposed methods are illustrated by numerical examples.