Ketercapaian dan Keterkontrolan Sistem Deskriptor Diskrit Linier Positif

  • Yulia Retno Sari Universitas Putra Indonesia “YPTK” Padang
Keywords: Inverse Drazin; Discrete positive descriptor system; Non negative matrix; Nilpotent matrix; Achieved properties


A positive discrete descriptor system has been widely used in modeling economics, engineering, chemistry and others. In this research, we studied the necessary conditions and sufficient conditions for a positive discrete descriptors system is achieved positive and controlled postively. In addition, it is also studied on sufficient terms and conditions which ensure that discrete systems are null controlled. By using linear algebraic method and Inverse Drazin, this research has proved several theorems for discrete descriptors system achieved positive, controlled positively and controlled null. In addition, examples are given as illustrations to reinforce the validity of the proven theorems.


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[1] Anton, H. Aljabar Linier Elementer Edisi Kedelapan-Jilid 1. Erlangga. Jakarta (2004)
[2] Arifin, A. Aljabar Linear Edisi Kedua, Penerbit ITB. Bandung (200)
[3] Bru, R., Coll, C., Sanchez, E. Structural Properties of Positive Linear Time-Invariant Difference-Algebraic Equations. Lin. Alg. Appl. Vol. 349 pp: 1-10 (2002)
[4] Campbell, S.L., Meyer. C.D. and J.R. Nicholas. Applications of the Drazin Invers to Linier Systems of Differential Equations with Singular Constant Coefficients. SIAM J. Appl. Math. Vol. 31 no. 3 pp: 411-425 (1979)
[5] Canto, B., Coll, C., Sanchez, E. Positive Solutions of a Discrete-Time Descriptor System. International Journal of Systems Science. Vol. 39 no. 1 pp: 81-88 (2008)
[6] Gantmacher, F.R. The Theory of Matrices. Vol 1. AMS Chelsea Publishing. Rhode Island (2000)
[7] Hoffman, K., Kunze, R. Linear Algebra Second Edition. New Jersey (2006)
[8] Jacob, Bill. Linear Algebra. W. H. Freeman and Company. New York (1990)
[9] Kaczorek. T. Linier Control Systems. Vol. 1. Research Studies Press LTD. England (1992)
[10] Noutsos, D., Tsatsomeros, M.J. Reachability and Holdability of Nonnegative States. SIAM Journal on Matrix Analysis and Applications. Vol. 30 pp: 700-712 (2008)
[11] Rahmalina, Widdya. Thesis, Sistem Deskriptor Diskrit Positif, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Andalas, Padang, 2011
[12] Retno Sari, Yulia. Sistem Deskriptor Diskrit Linier Positif yang Terkontrol Null. Journal Proceeding Seminar Nasional Matematika STKIP PGRI. Padang, 2015
[13] Roman, S. Advance Linear Algebra. Springer. New York, (1992)
[14] Serre, Denis. Matrices Theory and Application. Second Edition. Springer. France (2010)