Stability criteria for Volterra integrodynamic system (Q277707)

Summary: We study conditions under which the solutions of linear Volterra integrodynamic system of the form \(y^{\operatorname{\Delta}} \left(t\right) = A \left(t\right) y \left(t\right) + \int_{t_0}^t K \left(t, s\right) y \left(s\right) \operatorname{\Delta} s\) are stable on certain time scales. We construct a number of Lyapunov functionals on time scales from which we obtain necessary and sufficient conditions for stability of Volterra integrodynamic system and also we prove several results concerning qualitative behavior of this system.