Pointwise completeness and pointwise degeneracy of positive fractional descriptor continuous-time linear systems with regular pencils

Abstract

Pointwise completeness and pointwise degeneracy of positive fractional descriptor continuous-time linear systems with regular pencils are addressed. Conditions for pointwise completeness and pointwise degeneracy of the systems are established and illustrated by an example.

Analysis of the pointwise completeness and the pointwise degeneracy of the standard and fractional descriptor linear systems and electrical circuits

“…In a similar way as for standard systems we may defined for the fractional system (35) the matrices (3b), the Drazin inverse matrix D E satisfying (4) and the matrices (6). By Theorem 1 the matrices P and Q satisfy the conditions (7). Theorem 9.…”

“…A system, which is not pointwise complete is called pointwise degenerated. The pointwise completeness and pointwise degeneracy of linear continuous-time systems with delays have been investigated in [2,3,8,10,12], the pointwise completeness of linear discrete-time cone systems with delays in [13] and of fractional linear systems in [1,[6][7][8]. The pointwise completeness and pointwise degeneracy of standard and positive hybrid systems described by the general model have been analyzed in [4] and of positive linear systems with state-feedbacks in [5].…”

Bulletin of the Polish Academy of Sciences: Technical Sciences

“…The pointwise completeness and pointwise degeneracy of continuous-time linear systems with delays have been investigated in [1][2][3], the pointwise completeness of discrete-time linear systems with delays in [4,5] and of fractional linear systems in [6][7][8][9]. The pointwise completeness and the pointwise degeneracy of standard and positive hybrid systems described by the general model have been analyzed in [10] and of positive linear systems with state-feedbacks in [11].…”

“…Some new results in fractional systems have been given in [3,[12][13][14][15][16]17]. The Drazin inverse of matrices has been applied to the analysis of pointwise completeness and of pointwise degeneracy of the descriptor continuous-time and discrete-time linear systems in [18,19] and for fractional standard descriptor continuous-time linear systems in [20] and discrete-time linear systems in [7].…”

Bulletin of the Polish Academy of Sciences: Technical Sciences

“…A system, which is not pointwise complete is called pointwise degenerated. The pointwise completeness and pointwise degeneracy of linear continuous-time systems with delays have been investigated in [2,3,9,15,17], the pointwise completeness of linear discrete-time cone systems with delays in [18] and of fractional linear systems are presented in [1,9,10]. The pointwise completeness and pointwise degeneracy of standard and positive hydrid systems described by the general model have been analyzed in [7] and of positive linear systems with state-feedbacks in [8].…”