Application of the Drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencils

Descriptor (singular) linear systems were considered in many papers and books (Bru et al., 2000; 2002; 2003; Campbell et al., 1976; Dai, 1989; Dodig and Stosic, 2009; Fahmy and O’Reill, 1989; Kaczorek, 1992; 2004; 2007b; 2011a; 2011d; Van Dooren, 1979; Virnik, 2008). The eigenvalues and invariants assignment by state and output feedbacks were investigated by Fahmy and O’Reill (1989), Gantmacher (1960), Kaczorek (2004) as well as Kucera and Zagalak (1988), and the realization problem for singular positive continuous-time systems with delays was examined by Kaczorek (2007b). The computation of Kronecker’s canonical form of the singular pencil was analyzed by Van Dooren (1979). Positive linear systems with different fractional orders were addressed by Kaczorek (2010), who also discussed selected problems of fractional linear systems theory (Kaczorek, 2011b).