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

Bru, R. , Coll, C., Romero-Vivo S. and Sanchez, E. (2003). Some problems about structural properties of positive descriptor systems, in L. Benvenuti, A. Santis and L. Farina (Eds.), Positive Systems, Lecture Notes in Control and Information Sciences, Vol. 294, Springer, Berlin, pp. 233-240.10.1007/978-3-540-44928-7_32Search in Google Scholar

Bru, R., Coll, C. and Sanchez, E. (2000). About positively discrete-time singular systems, in N.E. Mastorakis (Ed.) System and Control: Theory and Applications, Electrical and Computer Engineering Series, World Scientific and Engineering Society, Athens, pp. 44-48.Search in Google Scholar

Bru, R., Coll, C. and Sanchez, E. (2002). Structural properties of positive linear time-invariant difference-algebraic equations, Linear Algebra and Applications 349(1-3): 1-10.10.1016/S0024-3795(02)00277-XSearch in Google Scholar

Campbell, S.L.,Meyer, C.D. and Rose, N.J. (1976). Applications of the Drazin inverse to linear systems of differential equations with singular constant coefficients, SIAM Journalon Applied Mathematics 31(3): 411-425.10.1137/0131035Search in Google Scholar

Commalut, C. and Marchand, N. (2006). Positive Systems, Lecture Notes in Control and Information Sciences, Vol. 341, Springer-Verlag, Berlin.Search in Google Scholar

Dai, L. (1989). Singular Control Systems, Lectures Notes in Control and Information Sciences, Vol. 118, Springer-Verlag, Berlin.Search in Google Scholar

Dodig, M. and Stosic, M. (2009). Singular systems state feedbacks problems, Linear Algebra and Its Applications431(8): 1267-1292.10.1016/j.laa.2009.04.024Search in Google Scholar

Fahmy, M.H, and O’Reill, J. (1989). Matrix pencil of closed-loop descriptor systems: Infinite-eigenvalues assignment, International Journal of Control 49(4): 1421-1431.10.1080/00207178908559713Search in Google Scholar

Farina, L. and Rinaldi, S. (2000). Positive Linear Systems, J. Willey, New York, NY.Search in Google Scholar

Gantmacher, F.R. (1960). The Theory of Matrices, Chelsea Publishing Co., New York, NY.Search in Google Scholar

Kaczorek, T. (1992). Linear Control Systems, Vol. 1, Research Studies Press, J. Wiley, New York, NY.Search in Google Scholar

Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London.10.1007/978-1-4471-0221-2Search in Google Scholar

Kaczorek, T. (2004). Infinite eigenvalue assignment by an output/feedback for singular systems, International Journalof Applied Mathematics and Computer Science 14(1): 19-23.Search in Google Scholar

Kaczorek, T. (2007a). Polynomial and Rational Matrices. Applicationsin Dynamical Systems Theory, Springer-Verlag, London.10.1007/978-1-84628-605-6Search in Google Scholar

Kaczorek, T. (2007b). Realization problem for singular positive continuous-time systems with delays, Control and Cybernetics36(1): 47-57.Search in Google Scholar

Kaczorek, T. (2010). Positive linear systems with different fractional orders, Bulletin of the Polish Academy of Sciences:Technical Sciences 58(3): 453-458.10.2478/v10175-010-0043-1Search in Google Scholar

Kaczorek, T. (2011a). Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm, Archivesof Control Sciences 21(3): 287-298.10.2478/v10170-010-0044-1Search in Google Scholar

Kaczorek, T. (2011b). Selected Problems of Fractional SystemsTheory, Springer-Verlag, Berlin.10.1007/978-3-642-20502-6Search in Google Scholar

Kaczorek T. (2011c). Singular fractional discrete-time linear systems, Control and Cybernetics 40(3): 1-8.10.1007/978-3-642-20502-6_1Search in Google Scholar

Kaczorek T. (2011d). Reduction and decomposition of singular fractional discrete-time linear systems, Acta Mechanica etAutomatica 5(4): 1-5.Search in Google Scholar

Kucera, V. and Zagalak, P. (1988). Fundamental theorem of state feedback for singular systems, Automatica 24(5): 653-658.10.1016/0005-1098(88)90112-4Search in Google Scholar

Van Dooren, P. (1979). The computation of Kronecker’s canonical form of a singular pencil, Linear Algebra andIts Applications 27: 103-140.10.1016/0024-3795(79)90035-1Search in Google Scholar

Virnik, E. (2008). Stability analysis of positive descriptor systems, Linear Algebra and Its Applications 429(10): 2640-2659.10.1016/j.laa.2008.03.002Search in Google Scholar