Existence of Î¨-Bounded Solutions for Linear Matrix Diï¬€erence Equations on Z+

G. Suresh; Ch Vasavi; T.S. Rao; M.S.N. Murty

doi:10.4067/S0719-06462014000100004

Authors

G. Suresh Koneru Lakshmaiah University, Department of Mathematics, Vaddeswaram, Guntur dt., A.P., India.
Ch Vasavi Koneru Lakshmaiah University, Department of Mathematics, Vaddeswaram, Guntur dt., A.P., India.
T.S. Rao Koneru Lakshmaiah University, Department of Mathematics, Vaddeswaram, Guntur dt., A.P., India.
M.S.N. Murty Acharya Nagarjuna University, Department of Mathematics, Nagarjuna Nagar-522510, Guntur dt., A.P., India.

DOI:

https://doi.org/10.4067/S0719-06462014000100004

Keywords:

Difference Equations, Fundamental Matrix, Î¨-bounded, Î¨-summable, Kronecker product

Abstract

This paper deals with obtaining necessary and suï¬ƒcient conditions for the existence of at least one Î¨-bounded solution for the linear matrix diï¬€erence equation X(n + 1) = A(n)X(n)B(n) + F(n), where F(n) is a Î¨-summable matrix valued function on Z⁺. Finally, we prove a result relating to the asymptotic behavior of the Î¨-bounded solutions of this equation on Z⁺.