Solutions of a class of singular linear systems of difference equations. Part 1
Languages of publication
We extend results of Campbell, Meyer, Jr. and Rose of applications of the Drazine inverse to linear systems of differential equations with singular constant coefficients to solutions of linear systems of difference equations A x_(n+1)+B x_n= f_n ,n≥0 when A and B are m×m complex matrices and may both singular, under conditions that rank(A)=1 and trace of A is not equal zero. f_n is an arbitrary function in C^m, and x_n∈C^m. We give a new closed form for all solutions of those systems when they are tractable, using the theory of the Drazin inverse, and a matrix K∈C^(m×m).
-  I. K. Dassios, On non-homogeneous linear generalized linear discrete time systems, Circuits Systems and Signal Processing, 31 (2012) 1699-1712
-  I. Dassios, G. Kalogeropoulos. On a non-homogeneous singular linear discrete time system with a singular matrix pencil. Circuits Syst Signal Process, 32 (2013) 1615-1635
-  I. K. Dassios, On a boundary value problem of a class of generalized linear discrete-time systems, Advances in Difference Equations, 2011: 51 (2011)
-  A. A. Soliman, Stability analysis of difference systems via cone valued Liapunov`s function method, J. Math. Kyoto Univ. 46 (2006) 65-74.
-  S. Zhang, Stability analysis of delay difference systems, Comput. Math. Appl. 33 (1997) 41-52.
-  P. K. Anh, L. C. Loi, On multipoint boundary-value problems for linear implicit non-autonomous systems of difference equations, Vietnam of Mathematics, 29 (2001) 281-286
-  C. Peng, Z. Cheng-Hui, Indefinite linear quadratic optimal control problem for singular linear discrete-time system: Krein space method. Acta Automatica Sinica 33 (2007) 635-639
-  I. K. Dassios, D. I. Baleanu, On a singular system of fractional nabla difference equations with boundary conditions, Boundary Value Problems, 2013: 148 (2013)
-  I. K. Dassios, On stability and state feedback stabilization of singular linear matrix difference equations, Advances in Differential Equations, 2012: 75 (2012)
-  S. L. Campbell, Limit Behavior of Solutions of Difference Equations, Linear Algebra and its Applications, 23 (1979) 167-178
-  P. K. Anh, H. T. N. Yen, On the Solvability of Initial-Value Problems for Nonlinear Implicit Difference Equations. Advances in Difference Equations volume 2004, Article number: 390451 (2004)
-  P. K. Anh, N. H. Du, and L. C. Loi, Connections Between Implicit Difference Equations and Differential -Algebraic Equations. Acta Mathematica Vietnamica 29 (2004) 23-39
-  P. K. Anh, D. S. Hoang, Stability of a Class of Singular Difference Equations, International Journal of Difference Equations, 1 (2006) 181-193
-  P. K. Anh, N. H. Du, and L. C. Loi, Singular Difference Equations: An Overview, Vietnam Journal of Mathematics, 35 (2007) 339-372
-  S. Hristova, A. Golev, K. Stefanova, Quasilinearization of the initial value problems for difference equations with "maxima". J. Appl. Math. 2012 (2012), 17 pages.
-  A. M. Kanan, K. Hassan, Solution of linear systems of differential equations with singular constant coefficients by the Drazin inverse of matrices, World Scientific News 137 (2019) 229-236
-  S. L. Campbell, C. D. Meyer, Jr., and N. J. Rose, Applications of the Drazin inverse to Linear Systems of differential equations with Singular Constant Coeffficients, SIAM J. Appl. Math. 31 (1976) 411-425
-  P. Wang, X. Liu, The quadratic convergence of approximate solutions for singular difference systems of differential equations with "maxima". J. Math. Computer Sci. 16 (2016) 227-238
-  P. Wang, X. Liu, T. Li, The rapid convergence for nonlinear singular differential systems with "maxima", J. Nonlinear Sci. Appl. 10 (2017) 5402-5421
-  S. L. Campbell, The Drazin inverses of an infinite matrix, SIAM J. Appl. Math. 31 (1976) 492-503
Publication order reference