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Paper details
Number 4 - December 2020
Volume 30 - 2020
Pointwise completeness and pointwise degeneracy of fractional standard and descriptor linear continuous-time systems with different fractional orders
Tadeusz Kaczorek, Łukasz Sajewski
Abstract
Descriptor and standard linear continuous-time systems with different fractional orders are investigated. Descriptor systems
are analyzed making use of the Drazin matrix inverse. Necessary and sufficient conditions for the pointwise completeness
and pointwise degeneracy of descriptor continuous-time linear systems with different fractional orders are derived. It is
shown that (i) the descriptor linear continuous-time system with different fractional orders is pointwise complete if and
only if the initial and final states belong to the same subspace, (ii) the descriptor linear continuous-time system with
different fractional orders is not pointwise degenerated in any nonzero direction for all nonzero initial conditions. Results
are reported for the case of two different fractional orders and can be extended to any number of orders.
Keywords
descriptor system, fractional system, noncommensurate order, pointwise completeness, pointwise degeneracy