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

Abstract

In this paper, we study the existence criteria for Ψ-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 Ψ-bounded solution for Sylvester matrix dynamical systems on time scales, for every Lebesgue Ψdeltaintegrable function F, on time scale T +. Further, we obtain a result relating to asymptotic behavior of Ψ-bounded solutions of this equation. The results are illustrated with suitable examples.

Controllability, Observability, and Stability aspects of matrix Sylvester Volterra Integro-Dynamical System on Time Scales

“…In [18] existence, uniqueness and Ulma's types stability of VIDS, stability criteria for nonlinear VIDS [19], and stability and controllability of VIDS [20]. In [6], examined the necessary and sufficient conditions are specified for the ψ-bounded solution on time scales.…”