On some class of periodic-discrete homogeneous difference equations via Fibonacci sequences. Issue 9 (1st September 2016)

• Record Type: Journal Article
• Authors: Ben Taher, R.; Benkhaldoun, H.; Rachidi, M.
• Is Part Of: Journal of difference equations and applications. Volume 22:Issue 9(2016)
• Page Start: 1292
• Page End: 1306
• Publication Date: 2016-09-01
• Subjects: Powers of a square matrix -- periodic discrete-time linear systems -- homogeneous linear difference equations -- generalized Fibonacci sequences; 11B39 -- 39A06 -- 93C55; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2016.1194407
• Languages: English
• ISSNs: 1023-6198

Abstract

Abstract : The intent of this paper is to solve the homogeneous linear difference equations with periodic coefficients. For this purpose, we turn our study in solving a class of discrete-time linear systems, in the algebra of square matrices. The tools used repose predominately on the combinatorial properties of the generalized Fibonacci sequences in the algebra of square matrices. Some explicit solutions are established and special cases are discussed. Illustrative examples are given.