Duality of singular linear systems of fractional nabla difference equations

被引:23
|
作者
Dassios, Ioannis K. [1 ,2 ]
Baleanu, Dumitru I. [3 ,4 ]
机构
[1] Univ Limerick, Dept Math & Stat, MACSI, Limerick, Ireland
[2] Univ Coll Dublin, Elect Res Ctr, ERC, Dublin, Ireland
[3] Cankaya Univ, Dept Math & Comp Sci, Ankara, Turkey
[4] Inst Space Sci, Magurele, Romania
基金
爱尔兰科学基金会;
关键词
Fractional nabla operator; Initial conditions; Singular systems; Difference equations; Linear discrete time system; Duality; TIME; CONTROLLABILITY;
D O I
10.1016/j.apm.2014.12.039
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
The main objective of this article is to provide a link between the solutions of an initial value problem of a linear singular system of fractional nabla difference equations, its proper dual system and its transposed dual system. By taking into consideration the case that the coefficients are square constant matrices with the leading coefficient singular, we study the prime system and by using the invariants of its pencil we give necessary and sufficient conditions for existence and uniqueness of solutions. After we prove that by using the pencil of the prime system we can study the existence and uniqueness of solutions of the proper dual system and the transposed dual system. Moreover their solutions, when they exist, can be explicitly represented without resorting to further processes of computations for each one separately. Finally, numerical examples are given based on a singular fractional nabla real dynamical system to justify our theory. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码:4180 / 4195
页数:16
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