caa a22 4500 606205055 CHVBK 20210128101005.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s00034-014-9930-2 doi (NATIONALLICENCE)springer-10.1007/s00034-014-9930-2 Dassios Ioannis MACSI, Department of Mathematics & Statistics, University of Limerick, Limerick, Ireland aut Optimal Solutions for Non-consistent Singular Linear Systems of Fractional Nabla Difference Equations [Elektronische Daten] [Ioannis Dassios] In this article, we study optimal solutions for a class of non-consistent singular linear systems of fractional nabla difference equations whose coefficients are constant matrices. We take into consideration the cases that the matrices are square with the leading coefficient singular, non-square and square with a matrix pencil which has an identically zero determinant. Then, first we study the system with given non-consistent initial conditions and provide optimal solutions. Furthermore, we consider the system with boundary conditions and provide optimal solutions for two cases, when the boundary value problem is non-consistent and when it has infinite solutions. Finally, we study the Kalman filter for singular non-homogeneous linear control systems of fractional nabla difference equations. Numerical examples are given to justify our theory. Springer Science+Business Media New York, 2014 Singular systems nationallicence Fractional calculus nationallicence Nabla operator nationallicence Difference equations nationallicence Linear nationallicence Discrete time system nationallicence Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/6(2015-06-01), 1769-1797 0278-081X 34:6<1769 2015 34 34 https://doi.org/10.1007/s00034-014-9930-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00034-014-9930-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Dassios Ioannis MACSI, Department of Mathematics & Statistics, University of Limerick, Limerick, Ireland aut NATIONALLICENCE 773 0- Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/6(2015-06-01), 1769-1797 0278-081X 34:6<1769 2015 34 34