Existence of Ψ-bounded solutions for sylvester matrix dynamical systems on time scales

Abstract

In this paper, we study the existence criteria for ?-bounded solutions of Sylvester matrix dynamical systems on time scales. The advantage of studying this system is it unifies continuous and discrete systems. First, we prove a necessary and sufficient condition for the existence of atleast one ?-bounded solution for Sylvester matrix dynamical systems on time scales, for every Lebesgue ?-deltaintegrable function F, on time scale T+. Further, we obtain a result relating to asymptotic behavior of ?-bounded solutions of this equation. The results are illustrated with suitable examples.