EXISTENCE OF Ψ-BOUNDED SOLUTIONS FOR LINEAR MATRIX DIFFERENCE EQUATIONS ON Z+

摘要

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