On properties of pointwise degenerate linear autonomous control systems. I

Метельский, А. В.; Karpuk, V. V.

doi:10.1134/s0005117909100038

Cited by 6 publications

(1 citation statement)

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“…A system which is not pointwise complete is called pointwise degenerated. These properties were studied in many works (Kaczorek, 2011;Korobov, 2017;Metel'skii and Karpuk, 2009). The pointwise completeness and pointwise degeneracy of fractional linear continuous-time systems were investigated by Kaczorek (2015) or Kaczorek and Busłowicz (2009), and for systems with different fractional orders by Trzasko (2014).…”

Section: Introductionmentioning

confidence: 99%

Pointwise completeness and pointwise degeneracy of fractional standard and descriptor linear continuous-time systems with different fractional orders

Kaczorek

Sajewski

2020

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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.

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